在此論文中，我們首先在第一章描述在半無限維規劃及無限維規劃上一些已知的結果。我們討論半無限維及無限維線性規劃的對偶理論及最佳化條件，並且也提及此類規劃問題的應用。更進一步，我們在此章節裡探討半無限維非線性規劃的一階最佳化條件，最後介紹一些解半無限維規劃的常用演算法。

在第二章中，我們呈現一個解半無限維非線性規劃的演算法。為了處理非線性的限制式，我們利用一個適當的鬆弛凸化法來逼近非線性限制函數。接下來，我們結合切面法與鬆弛凸化法的想法，進而提出一個新的演算法來解非線性半無限維規劃問題。在一些給定的誤差下，我們的方法將被證明在有限步驟內停止並得一個近似解。除此之外, 在此章中也會利用我們提出的方法來解一些測試問題及半無限維非線性規劃的應用問題。

接下來，第三章將會討論在L1空間上的無限維線性規劃問題(PL)，此類問題是相關於一種稱為廣義容量問題的最佳化問題。因為(PL)的最佳解並不存在，故我們藉由解廣義容量問題來逼近無限維線性規劃問題(PL)的最佳值，我們也會在此章節內給出原問題最佳值與算法得到之近似最佳值的誤差估計。更進一步，我們的方法將被推廣到在L1空間上的無限維二次規劃問題(PQ)，也會發現(PL)與(PQ)之間有些類似的結果。(PL)與(PQ)的數值計算結果也會呈現在第三章裡並且會與離散法進行比較進而展現我們算法較有計算效率。

最後在第四章，對於在半無限維規劃問題及無限維線性及二次規劃問題上，我們將會給出結論並且提及一些未來可進行之研究方向。

In this dissertation, we firstly present some well-known results in the semi-infinite and infinite programs in Chapter 1. We investigate the duality theory and optimality conditions for linear semi-infinite and infinite programs.
Some applications of the linear semi-infinite and infinite programs are addressed too. Moreover, the first-order optimality conditions for the nonlinear semi-infinite programs (SIP) are also discussed in this chapter. In the final of Chapter 1, we introduce some popular methods for solving the SIP problems.

In Chapter 2, we present an algorithm to solve nonlinear SIP problems. To deal with the nonlinear constraint, we use an adaptive convexification relaxation to approximate the nonlinear constraint function. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve the nonlinear SIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the problems. In addition, the test problems and some application examples of nonlinear SIP problems are implemented by the method proposed in this chapter.

Next, an infinite-dimensional linear programming formulated on L1 spaces, problem (PL), is studied in Chapter 3. This problem is related to the optimization problem, general capacity problem. We approach the optimal value for problem (PL) via solving the general capacity problem since the optimal solution does not exist in problem (PL). The error bound for the difference of our approach is also given in this chapter. Furthermore, we extend the concept of our algorithm to solve the infinite quadratic programs in L1 spaces, (PQ). We can find that there are some similar results between problems (PL) and (PQ). Numerical examples for problems (PL) and (PQ) are also implemented and compared with the discretization method to show our computational efficiency.

Finally, we make some conclusions on the nonlinear SIP problems and infinite programs in L1 spaces in Chapter 4.
The further studies for our proposed methods are also mentioned in this chapter.

[1] C. S. Adjiman, I. P. Androulakis, and C. A. Floudas, A global optimization method, αBB, for general twice-differentiable constrained NLPs - I: Theoretical advances, Computers and Chemical Engineering, vol. 22, pp. 1137–1158, 1998.
[2] C. S. Adjiman, I. P. Androulakis, and C. A. Floudas, A global optimization method, αBB, for general twice-differentiable constrained NLPs - II: Implementation and computational results, Computers and Chemical Engineering, vol. 22, pp. 1159–1179, 1998.
[3] E. J. Anderson, A review of duality theory for linear programming over topological vector space, Journal of Mathematical Analysis and Applications, vol. 97, pp. 380–392, 1983.
[4] E. J. Anderson and P. Nash, Linear programming in infinite-dimensional spaces: theory and applications. John Wiley & Sons, 1987.
[5] E. J. Anderson and A. Philpott, Duality and an algorithm for a class of continuous transportation problems, Mathematics of Operations Research, vol. 9, pp. 222–231, 1984.
[6] A. Auslender, M. A. Goberna, and M. A. López, Penalty and smoothing methods for convex semi-infinite programming, Mathematics of Operations Research, vol. 34, pp. 303–319, 2009.
[7] R. E. Bellman, Dynamic Programming. Princeton University Press, N.J., 1957.
[8] A. Ben Tal, L. Kerzner, and S. Zlobec, Optimality conditions for convex semiinfinite programming problems, Naval Research Logistics, vol. 27, pp. 413–435, 1980.
[9] B. Betrò, An accelerated central cutting plane algorithm for linear semi-infinite programming, Mathematical Programming, vol. 101, pp. 479–495, 2004.
[10] B. Bhattacharjee, W. H. Green Jr., and P. I. Barton, Interval methods for semiinfinite programs, Computational Optimization and Applications, vol. 30, pp. 63–93, 2005.
[11] B. Bhattacharjee, P. Lemonidis, W. H. Green Jr., and P. I. Barton, Global solution of semi-infinite programs, Mathematical Programming, vol. 103, pp. 283–307, 2005.
[12] C. G. L. Bianco and A. Piazzi, A hybrid algorithm for infinitely constrained optimization, International Journal of Systems Science, vol. 32, pp. 91–102, 2001.
[13] J. F. Bonnans, R. Cominetti, and A. Shapiro, Second order optimality conditions based on parabolic second order tangent sets, SIAM Journal on Optimization, vol. 9, pp. 466–492, 1999.
[14] J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, 2000.
[15] J. M. Borwein, Direct theorems in semi-infinite convex programming, Mathematical Programming, vol. 21, pp. 301–318, 1981.
[16] J. M. Borwein, Semi-infinite programming duality: how special is it? in Semi-Infinite Programming and Applications, ser. Lecture Notes in Economics and Mathematical Systems, A. V. Fiacco and K. O. Kortanek, Eds. Springer, Berlin, 1983.
[17] R. I. Bot and G. Wanka, An alternative formulation for a new closed cone constraints qualification, Nonlinear Analysis, vol. 64, pp. 1367–1381, 2006.
[18] M. J. Cánovas, A. Hantoute, M. A. López, and J. Parra, Stability of indices in the KKT conditions and metric regularity in convex semi-infinite optimization, Journal of Optimization Theory and Applications, vol. 139, pp. 485–500, 2008.
[19] M. J. Cánovas, M. A. López, and J. Parra, Stability in the discretization of a parametric semi-infinite convex inequality system, Mathematics of Operations Research, vol. 27, pp. 755–774, 2002.
[20] R. M. Chanberlain, M. J. D. Powell, C. Lemarechal, and H. C. Pedwesen, The watchdog technique for forcing convergence in algorithms for constrained optimization, Mathematical Programming Study, vol. 16, pp. 1–17, 1982.
[21] A. Charnes, W. W. Cooper, and K. O. Kortanek, Duality in semi-infinite programs and some works of Haar and Carathéodory, Management Science, vol. 9, pp. 209–228, 1963.
[22] S. Y. Chen, Algorithms for semi-infinite transportation problems and quadratic infinite Lp problems, Ph.D. dissertation, National Cheng Kung University, 2008.
[23] S. Y. Chen and S. Y. Wu, Algorithms for infinite quadratic programming in Lp spaces, Journal of Computational and Applied Mathematics, vol. 213, pp. 408–422, 2008.
[24] G. Choquet, Theory of capacities, Annales de l’Institut Fourier, vol. 5, pp. 131–295, 1954.
[25] S. Clark, An infinite-dimensional LP duality theorem, Mathematics of Operations Research, vol. 28, pp. 233–245, 2003.
[26] I. D. Coope and G. A. Watson, A projected Lagrangian algorithm for semi-infinite programming, Mathematical Programming, vol. 32, pp. 337–356, 1985.
[27] M. A. Dahleh and I. J. Diaz-Bobillo, Control of uncertain systems: a linear programming approach. Prentice-Hall, Englewood Cliffs, N.J., 1995.
[28] M. A. Dahleh and J. B. Pearson Jr., l1-optimal compensators for continuous-time systems, IEEE Transaction on Automatic Control, vol. 32, pp. 889–895, 1987.
[29] G. B. Dantzig, Linear programming and extensions. Princeton University Press, N. J., 1963.
[30] G. B. Dantzig and M. N. Thapa, Linear programming 1: Introduction. Springer, New York, 1997.
[31] R. J. Duffin, Infinite programs, in Linear Inequalities and Related Systems, H. W. Kukn and A. W. Tucker, Eds. Princeton University Press, N.J., 1956.
[32] R. J. Duffin and L. A. Karlovitz, An infinite linear program with a duality gap, Management Science, vol. 12, pp. 122–134, 1965.
[33] S. C. Fang, C. J. Lin, and S. Y. Wu, Solving quadratic semi-infinite programming problems by using relaxed cutting-plane scheme, Journal of Computational and Applied Mathematics, vol. 129, pp. 89–104, 2001.
[34] E. Feinberg and A. Shwartz, Constrained discounted dynamic programming. Mathematics of Operations Research, vol. 21, pp. 922–945, 1996.
[35] L. Finlay, V. Gaitsgory, and I. Lebedev, Linear programming solutions of periodic optimization problems: approximation of the optimal control, Journal of Industrial and Management Optimization, vol. 3, pp. 399–413, 2007.
[36] C. A. Floudas, Deterministic Global Optimization, Theory, Methods and Applications. Kluwer, Dordrecht, 2000.
[37] C. A. Floudas and O. Stein, The adaptive convexification algorithm: a feasible point method for semi-infinite programming, SIAM Journal on Optimization, vol. 18, pp. 1187–1208, 2007.
[38] B. Fugled, On the theory of potentials in locally compact spaces, Acta Mathematica, vol. 103, pp. 139–215, 1960.
[39] J. Fülöp, A semi-infinite programming method for approximating load duration curves by polynomials, Computing, vol. 49, pp. 201–212, 1992.
[40] J. R. Gabriel and O. Hernández-Lerma, Stong duality of the general capacity problem in metric spaces, Mathematical Methods of Operations Research, vol. 53, pp. 25–34, 2001.
[41] J. R. Gabriel, B. R. López-Martnez, and O. Hernández-Lerma, The lagrange approach to infinite linear programs, TOP, vol. 9, pp. 293–314, 2001.
[42] K. Glashoff, Duality theory of semi-infinite programming, in Semi-infinite programming, ser. Lecture Notes in Control and Information Sciences, R. Hettich, Ed. Springer, Berlin, 1979.
[43] K. Glashoff and S.-A. Gustafson, Linear Optimization and Approximation. Springer-Verlag, Berlin, 1983.
[44] M. A. Goberna, V. Jeyakumar, and M. A. Lópeza, Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities, Nonlinear Analysis, vol. 68, pp. 1184–1194, 2008.
[45] M. A. Goberna and V. Jornet, On Haar¡¦s dual problem, OR Spektrum, vol. 18, pp. 209–217, 1996.
[46] M. A. Goberna and M. A. López, Linear Semi-Infinite Optimization. John Wiley & Sons, Chichester, 1998.
[47] M. A. Goberna and M. A. López, On duality in semi-infinite programming and existence theorems for linear inequalities, Journal of Mathematical Analysis and Applications, vol. 230, pp. 173–192, 1999.
[48] M. A. Goberna and M. A. López, Linear semi-infinite programming theory: An updated survey, European Journal of Operational Research, vol. 143, pp. 390–405, 2002.
[49] J. A. Gómez, P. J. Bosch, and J. Amaya, Duality for inexact semi-infinite linear programming, Optimization, vol. 54, pp. 1–25, 2005.
[50] G. Gonzaga, E. Polak, and R. Trahan, An improved algorithm for optimization problems with functional inequality constraints, IEEE Transactions on Automatic Control, vol. AC-25, pp. 49–54, 1980.
[51] S. Görner, A. Potchinkov, and R. Reemtsen, The direct solution of nonconvex nonlinear FIR filter design problems by a SIP method, Optimization and Engineering, vol. 1, pp. 123–154, 2000.
[52] W. L. Gorr, S.-A. Gustafson, and K. O. Kortanek, Optimal control strategies for air quality standards and regulatory policy, Environment and Planning, vol. 4, pp. 183–192, 1972.
[53] G. Gramlich, R. Hettich, and E. W. Sachs, Local convergence of SQP methods in semi-infinite programming, SIAM Journal on Optimization, vol. 5, pp. 641–658, 1995.
[54] H. J. Greenberg, Mathematical programming models for environmental quality control, Operations Research, vol. 43, pp. 578–622, 1995.
[55] P. R. Gribik, A central cutting plane algorithm for semi-infinite programming problems, in Semi-Infinite Programming, ser. Lecture Notes in Control and Information Sciences, R. Hettich, Ed. Springer, Berlin, 1979.
[56] F. Guerra-Vázquez, J.-J. Rückmann, O. Stein, and G. Still, Generalized semiinfinite programming: A tutorial, Journal of Computational and Applied Mathematics, vol. 217, pp. 394–419, 2008.
[57] M. Gugat, Convex semi-infinite parametric programming: uniform convergence of the optimal value functions of discretized problems, Journal of Optimization Theory and Applications, vol. 101, pp. 191–201, 1999.
[58] M. Gugat, Error bounds for infinite systems of convex inequalities without Slater’s condition, Mathematical Programming, Series B, vol. 88, pp. 255–275, 2000.
[59] S. A. Gustafson, On the computational solution of a class of generalized moment problems, SIAM Journal on Numerical Analysis, vol. 7, pp. 343–357, 1970.
[60] S. A. Gustafson, K. O. Kortanek, and W. Rom, Non-Chebyshevian moment problems, SIAM Journal on Numerical Analysis, vol. 7, pp. 335–342, 1970.
[61] S. A. Gustafson and K. Kortanek, Numerical treatment of a class of semi-infinite programming problems, Naval Research Logistics Quarterly, vol. 20, pp. 477–504, 1973.
[62] F. J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform, in Proceedings of the IEEE, vol. 66, 1978.
[63] O. Hernández-Lerma and J. B. Lasserre, Approximation schemes for infinite linear programs, SIAM Journal on Optimization, vol. 8, pp. 973–988, 1998.
[64] R. Hettich, An implementation of a discretization method for semi-infinite programming, Mathematical Programming, vol. 34, pp. 354–361, 1986.
[65] R. Hettich and G. Gramlich, A note on the implementation of a method for quadratic semi-infinite programming, Mathematical Programming, vol. 46, pp. 249–254, 1990.
[66] R. Hettich and K. O. Kortanek, Semi-infinite programming: Theory, methods, and applications, SIAM Review, vol. 35, pp. 380–429, 1993.
[67] R. Hettich and G. Still, Semi-infinite programming models in robotics, in Parametric Optimization and Related Topics II, J. Guddat, H. T. Jongen, B. Kummer, and F. Nozicka, Eds. Akademie Verlag, Berlin, 1991.
[68] R. Hettich and G. Still, Semi-infinite programming: Second order optimality conditions, in Encyclopedia of Optimization, 2nd ed., C. A. Floudas and P. M. Pardalos, Eds. Springer, 2009.
[69] R. Hettich and W. van Honstede, On quadratically convergent methods for semiinfinite programming, in Semi-infinite Programming, R. Hettich, Ed. Springer, Berlin, 1979.
[70] R. Hettich and P. Zencke, Numerische Methoden der Approximation und semiinfiniten Optimierung. Teubner, Stuttgart, 1982.
[71] R. P. Hettich and H. T. Jongen, Semi-infinite programming: Conditions of optimality and applications, in Optimization Techniques, ser. Lecture Notes in Control and Information Sciences, J. Stoer, Ed. Springer, Berlin, 1978.
[72] H. Hu, A one-phase algorithm for semi-infinite linear programming, Mathematical Programming, vol. 46, pp. 85–103, 1990.
[73] L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica, vol. 26, pp. 371–375, 1990.
[74] J. B. Jian, Q. J. Xu, and D. L. Han, A norm-relaxed method of feasible directions for finely discretized problems from semi-infinite programming, European Journal of Operational Research, vol. 186, pp. 41–62, 2008.
[75] H. T. Jongen, P. Jonker, and F. Twilt, Critical sets in parametric optimization, Mathematical Programming, vol. 34, pp. 333–353, 1986.
[76] H. T. Jongen, J.-J. Rückmann, and G.-W. Weber, One-parametric semi-infinite optimization: on the stability of the feasible set, SIAM Journal on Optimization, vol. 4, pp. 637–648, 1994.
[77] H. T. Jongen, W. Wetterling, and G. Zwier, On sufficient conditions for local optimality in semi-infinite programming, Optimization, vol. 18, pp. 165–178, 1987.
[78] N. Kanzi and S. Nobakhtian, Optimality conditions for non-smooth semi-infinite programming, Optimization, vol. 59, pp. 717–727, 2010.
[79] D. F. Karney, Duality gaps in semi-infinite programming, an approximation problem, Mathematical Programming, vol. 20, pp. 129–143, 1981.
[80] H. Kawasaki, Second order necessary optimality conditions for minimizing a suptype function, Mathematical Programming, vol. 49, pp. 213–229, 1990.
[81] D. Klatte, Stable local minimizers in semi-infinite optimization: regularity and second-order conditions, Journal of Computational and Applied Mathematics, vol. 56, pp. 137–157, 1994.
[82] D. Klatte and R. Henrio, Regularity and stability in nonlinear semi-infinite optimization, in Semi-infinite Programming, R. Reemtsen and J. Rückmann, Eds. Kluwer, Dordrecht, 1998.
[83] K. O. Kortanek, On the 1962-1972 decade of semi-infinite programming: a subjective view, in Semi-infinite programming, ser. Nonconex Optimization and Its Applications, M. A. Goberna and M. A. López, Eds. Kluwer Academic Publishers, 2001.
[84] K. O. Kortanek and H. No, A central cutting plane algorithm for convex semiinfinite programming problems, SIAM Journal on Optimization, vol. 3, pp. 901–918, 1993.
[85] O. I. Kostyukova and T. V. Tchemisova, Sufficient optimality conditions for convex semi-infinite programming, Optimization Methods and Software, vol. 25, pp. 279–297, 2010.
[86] K. S. Kretschmer, Programmes in paired spaces, Canadian Journal of Mathematics, vol. 13, pp. 221–238, 1961.
[87] H. C. Lai and S. Y. Wu, Extremal points and optimal solutions for general capacity problems, Mathematical Programming, vol. 54, pp. 87–113, 1992.
[88] H. C. Lai and S. Y. Wu, On linear semi-infinite programming problems: An algorithm, Numerical Functional Analysis and Optimization, vol. 13, pp. 287–304, 1992.
[89] P. J. Laurent and C. Carasso, An algorithm of successive minimization in convex programming, R.A.I.R.O. Numerical Analysis, vol. 12, pp. 377–400, 1978.
[90] C. T. Lawrence and A. L. Tits, Feasible sequential quadratic programming for finely discretized problems from sip, in Semi-Infinite Programming, R. Reemtsen and J.-J. Ruckmann, Eds. Kluwer Academic Publishers, 1998.
[91] G. Y. Li and K. F. Ng, On extension of Fenchel duality and its application, SIAM Journal on Optimization, vol. 19, pp. 1489–1509, 2008.
[92] W. Li, C. Nahak, and I. Singer, Constraint qualifications in semi-infinite systems of convex inequalities, SIAM Journal on Optimization, vol. 11, pp. 31–52, 2000.
[93] W. Li and I. Singer, Asymptotic constraint qualifications and error bounds for semi-infinite systems of convex inequalities, in Semi-Infinite Programming: Recent Advances, M. A. Goberna and M. A. López, Eds. Kluwer, 2001.
[94] M. López and G. Still, Semi-infinite programming, European Journal of Operational Research, vol. 180, pp. 491–518, 2007.
[95] M. A. Lopez and E. Vercher, Convex semi-infinite games, Journal of Optimization Theory and Applications, vol. 50, pp. 289–312, 1986.
[96] D. G. Luenberger, Optimization by Vector Space Methods. John Wiley & Sons, 1969.
[97] D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming. Springer, 2008.
[98] G. Meinardus, Approximation of Functions: Theory and Numerical Methods. Springer, Berlin-Heidelberg New York, 1967.
[99] T. Nakamura and M. Yamasaki, Sufficient conditions for duality theorems in infinite linear programming problems, Hiroshima Mathematical Journal, vol. 9, pp. 323–334, 1979.
[100] Q. Ni, C. Ling, L. Qi, and K. L. Teo, A truncated projected Newton-type algorithm for large-scale semi-infinite programming, SIAM Journal on Optimization, vol. 16, pp. 1137–1154, 2006.
[101] S. Nordebo and Z. Q. Zang, Semi-infinite linear programming: A unified approach to digital filter design with timeand frequency-domain specifications, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, pp. 765–775, 1999.
[102] G. Nuernberger, Global unicity in semi-infinite optimization, Numerical Functional Analysis and Optimization, vol. 8, pp. 173–191, 1985.
[103] M. Ohtsuka, Generalized capacity and duality theorem in linear programming, Journal of Science, Hiroshima University Series A-I, vol. 30, pp. 45–56, 1966.
[104] S. Ozogur Akyuz and G.-W. Weber, On numerical optimization theory of infinite kernel learning, Journal of Global Optimization, vol. 48, pp. 215–239, 2010.
[105] T. W. Parks and C. S. Burrus, Digital Filter Design. Wiley, 1987.
[106] A. I. P. N. Pereiraa and E. M. G. P. Fernandes, A reduction method for semiinfinite programming by means of a global stochastic approach, Optimization, vol. 58, pp. 713–726, 2009.
[107] E. Polak, Optimization : Algorithms and Consistent Approximations. Springer, New York, 1997.
[108] A. Potchinkov and R. Reemtsen, FIR filter design in the complex domain by a semi-infinite programming technique: I. the method, Archiv für Elektronik und Übertragungstechnik, vol. 48, pp. 135–144, 1994.
[109] A. Potchinkov and R. Reemtsen, FIR filter design in the complex domain by a semi-infinite programming technique: II. examples, Archiv für Elektronik und Übertragungstechnik, vol. 48, pp. 200–209, 1994.
[110] A. Potchinkov and R. Reemtsen, The simultaneous approximation of magnitude and phase by FIR digital filters: Part 1. a new approach, International Journal of Circuit Theory and Applications, vol. 25, pp. 167–177, 1997.
[111] A. Potchinkov and R. Reemtsen, The simultaneous approximation of magnitude and phase by FIR digital filters: Part 2. methods and examples, International Journal of Circuit Theory and Applications, vol. 25, pp. 179–197, 1997.
[112] C. J. Price and C. J. Coope, Numerical experiments in semi-infinite programming, Computational Optimization and Applications, vol. 6, pp. 169–189, 1996.
[113] C. J. Price and I. D. Coope, An exact penalty function algorithm for semi-infinite programmes, BIT, vol. 30, pp. 723–734, 1990.
[114] M. C. Pullan, Convergence of a general class of algorithms for separated continuous linear programs, SIAM Journal on Optimization, vol. 10, pp. 722–731, 2000.
[115] L. Qi, C. Ling, X. J. Tong, and G. Zhou, A smoothing projected Newton-type algorithm for semi-infinite programming, Computational Optimization and Applications, vol. 42, pp. 1–30, 2009.
[116] L. Qi, S. Y. Wu, and G. Zhou, Semismooth Newton methods for solving semiinfinite programming problems, Journal of Global Optimization, vol. 27, pp. 215–232, 2003.
[117] R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems, Journal of Optimization Theory and Applications, vol. 71, pp. 85–103, 1991.
[118] R. Reemtsen, Some outer approximation methods for semi-infinite optimization problems, Journal of Computational and Applied Mathematics, vol. 53, pp. 87–108, 1994.
[119] R. Reemtsen and S. Görner, Numerical methods for semi-infinite programming: A survey, in Semi-Infinite Programming, R. Reemsten and J.-J. Rückmann, Eds. Kluwer Academic Publishers, Boston, MA, 1998.
[120] R. T. Rockafellar, Convex Analysis. Princeton University Press, N.J., 1970.
[121] R. T. Rockafellar, Conjugate duality and optimization. SIAM, Philadelphia, 1974.
[122] W. Rogosinsky, Moments of non-negative mass, Proceedings of the Royal Society of London - Series A, vol. 245, pp. 1–27, 1958.
[123] K. Roleff, A stable multiple exchange algorithm for linear SIP, in Semi-infinite Programming, ser. Lecture Notes in Control and Information Sciences, R. Hettich, Ed. Springer, Berlin, 1979.
[124] J.-J. Rückmann and A. Shapiro, Augmented Lagrangians in semi-infinite programming, Mathematical Programming, Series B, vol. 116, pp. 499–512, 2009.
[125] H. H. Schaefer, Topological vector spaces, 2nd ed. Springer, 1999.
[126] A. Shapiro, Second order derivatives of extremal value functions and optimality conditions for semi-infinite programs, Mathematics of Operations Research, vol. 10, pp. 207–219, 1985.
[127] A. Shapiro, On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints, SIAM Journal on Optimization, vol. 7, pp. 508–518, 1997.
[128] A. Shapiro, On duality theory of convex semi-infinite programming, Optimization, vol. 54, pp. 535–543, 2005.
[129] A. Shapiro, Semi-infinite programming, duality, discretization and optimality conditions, Optimization, vol. 58, pp. 133–161, 2009.
[130] T. Q. Son, J. J. Strodiot, and V. H. Nguyen, ε-optimality and ε-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints, Journal of Optimization Theory and Applications, vol. 141, pp. 389–409, 2009.
[131] O. Stein, A semi-infinite approach to design centering, in Optimization with Multivalued Mappings: Theory, Applications and Algorithms, S. Dempe and S. Kalashnikow, Eds. Springer, New York, 2006.
[132] O. Stein and A. Winterfeld, Feasible method for generalized semi-infinite programming, Journal of Optimization Theory and Applications, vol. 146, pp. 419–443, 2010.
[133] G. Still, Discretization in semi-infinite programming: the rate of convergence, Mathematical Programming, vol. 91, pp. 53–69, 2001.
[134] Y. Tanaka, M. Fukushima, and T. Ibaraki, A comparative study of several semiinfinite nonlinear programming algorithms, European Journal of Operational Research, vol. 36, pp. 92–100, 1988.
[135] Y. Tanaka, M. Fukushima, and T. Ibaraki, A globally convergent SQP method for semi-infinite nonlinear optimization, Journal of Computational and Applied Mathematics, vol. 23, pp. 141–153, 1988.
[136] R. A. Tapia and M. W. Trosset, An extension of the Karush-Kuhn-Tucker necessity conditions to infinite programming, SIAM Review, vol. 36, pp. 1–17, 1994.
[137] K. L. Teo, C. J. Goh, and K. H. Wong, A unified approach to optimal control problems. Longman Scientific & Technical, England, 1991.
[138] K. L. Teo, X. Q. Yang, and L. S. Jennings, Computational discretization algorithms for functional inequality constrained optimization, Annals of Operations Research, vol. 98, pp. 215–234, 2000.
[139] P. P. Vaidyanathan, Multirate systems and filter banks. Prentice Hall, Englewood Cliffs, NJ, 1993.
[140] R. J. Vanderbei, Extreme optics and the search for earth-like planets, Mathematical Programming, Series B, vol. 12, pp. 255–272, 2008.
[141] A. I. F. Vaz and E. C. Ferreira, Air pollution control with semi-infinite programming, Applied Mathematical Modelling, vol. 33, pp. 1957–1969, 2009.
[142] Z. Wan, S. Y. Wu, and K. L. Teo, Some properties on quadratic infinite programs of integral type, Applied Mathematics Letters, vol. 20, pp. 676–680, 2007.
[143] G. A. Watson, A multiple exchange algorithm for multivariate Chebyshev approximation, SIAM Journal on Numerical Analysis, vol. 12, pp. 46–52, 1975.
[144] G. Weiss, A simplex based algorithm to solve separated continuous linear programs, Mathematical Programming, vol. 115, pp. 151–198, 2008.
[145] C. Z. Wu and K. L. Teo, Global impulsive optimal control computation, Journal of Industrial and Management Optimization, vol. 2, pp. 435–450, 2006.
[146] C. Z. Wu, K. L. Teo, and Y. Zhao, Numerical method for a class of optimal control problems subject to non-smooth functional constraints, Journal of Computational and Applied Mathematics, vol. 217, pp. 311–325, 2008.
[147] S. Y. Wu, The general capacity problem, in Methods of Operations Research, W. Oettli et al., Ed. Oelgeschlager, Gunn and Hain, Cambridge, MA, 1985.
[148] S. Y. Wu, Extremal points and an algorithm for a class of continuous transportation problems, Journal of Information and Optimization Sciences, vol. 13, pp. 97–106, 1992.
[149] S. Y. Wu, A cutting plane approach to solving quadratic infinite programs on measure spaces, Journal of Global Optimization, vol. 21, pp. 67–87, 2001.
[150] S. Y. Wu and S. C. Fang, Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method, Computers and Mathematics with Applications, vol. 38, pp. 23–33, 1999.
[151] S. Y. Wu, S. C. Fang, and C. J. Lin, Relaxed cutting plane method for solving linear semi-infinite programming problems, Journal of Optimization Theory and Applications, vol. 99, pp. 759–779, 1998.
[152] S. Y. Wu, D. H. Li, L. Qi, and G. Zhou, An iterative method for solving KKT system of the semi-infinite programming, Optimization Methods and Software, vol. 20, pp. 629–643, 2005.
[153] M. Yamasaki, On a capacity problem raised in connection with linear programming, Journal of Science, Hiroshima University Series A-I, vol. 30, pp. 57–73, 1966.
[154] X. Q. Yang and K. L. Teo, Nonlinear Lagrangian functions and applications to semi-infinite programs, Annals of Operations Research, vol. 103, pp. 235–250, 2001.
[155] K. F. C. Yiu, M. J. Gao, T. J. Shiu, S. Y. Wu, T. Tran, and I. Claesson, An fast algorithm for the optimal design of high accuracy windows in signal processing, Tech. Rep., 2011.
[156] L. P. Zhang, S. Y. Wu, and M. A. López, A new exchange method for convex semi-infinite programming, SIAM Journal on Optimization, vol. 20, pp. 2959–2977, 2010.
[157] X. Y. Zheng and X. Q. Yang, Lagrange multipliers in nonsmooth semi-infinite optimization problems, Mathematics of Operations Research, vol. 32, pp. 168–181, 2007.
[158] U. Zimmermann, Duality for algebraic linear programming, Linear Algebra and its Applications, vol. 32, pp. 9–31, 1980.