本篇論文研究積分型式的無限維線性規劃問題，其中決策變數要落在Lp空間中，同時要求決策變數定義在一個緊緻區間上，並界於一個上界連續函數與一個下界連續函數之間。為了簡化原本的問題，我們轉換原問題成一個等價的問題來討論。在此我們發展兩個演算法來解這類型的問題，並證明演算法是收斂的。最後利用發展的演算法來解幾個數值例子。

This thesis studies the infinite-dimensional linear programming problems of integral type. The decision variable is taken in the Lp space where 1<p<infty and required to have an upper bound and a lower bound by continuous functions on a compact interval. To simplify the original problems, we transform them to equivalent problems. Two numerical algorithms are proposed for solving these problems and the convergence properties of the algorithms are given. Some numerical examples are also given to implement the proposed algorithms.

[1]E. J. Anderson and P. Nash, Linear programming in infinite-dimensional spaces, John Wiley and Sons, Chichester, 1987.
[2]R. Bellman, Dynamic Programming, Princeton University Press, Princeton, N. J., 1957.
[3]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.
[4]G. Choquet, Theory of capacities, Annales de l'Institut Fourier, Vol. 5 ,pp. 131-295, 1954.
[5]G. B. Dantzig, Linear Programming and Extensions, Princeton, NJ: Princeton University Press, 1963.
[6]G. B. Dantzig and M. N. Thapa, Linear programming 1: introduction, Springer, New York, 1997.
[7]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.
[8]P. R. Gribik, A central cutting plane algorithm for semi-infinite programming, in: R. Hettich(Ed.), Semi-infinite Programming, Springer, Berlin, pp. 6-82, 1979.
[9]R. Hettich, A review of numerical methods for semi-infinite optimization, in: A. V. Fiacco and K. O. Kortanek(Eds.), Semi-infinite Programming and Applications, Springer, Berlin, pp. 158-178, 1983.
[10]R. Hettich and K. O. Kortanek, Semi-infinite programming: theory, method and applications, SIAM Review, Vol. 35, pp. 380-429, 1993.
[11]S. Ito, S. Y. Wu, T. J. Shiu, and K. L. Teo, A numerical approach to infinite-dimensional linear programming in L1 spaces, Journal of industrial and management optimization, Vol. 6, pp. 15-28, 2010.
[12]D. G. Luenberger, Linear and nonlinear programming, Addison-Wesley, Massachusetts, 1984.
[13]H. C. Lai and S. Y. Wu, Extremal points and optimal solutions for general capacity problems, Mathematical Programming, Vol. 54, pp. 87-113, 1992.
[14]M. Ohtsuka, Generalized capacity and duality theorem in linear programming, Journal of Science, Hiroshima University Series A-I, Vol. 30, pp. 45-56, 1966.
[15]H. L. Royden, Real analysis, Prentice-Hall, New Jersey, 1988.
[16]W. Rudin, Functional analysis, McGraw-Hill, New York, 1973.
[17]W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1977.
[18]A. E. Taylor, Introduction to functional analysis, John Wiley and Sons, 1958.
[19]R. J. Vanderbei, Extreme optics and the search for Earth-like planets, Mathematical Programming, Vol. 112, pp. 255-272, 2007.
[20]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.
[21]S. Y. Wu, S. Fang, and C. J. Lin, Solving general capacity problem by relaxed cutting plane approach, Annals of Operations Research, Vol. 103, pp. 193-211, 2001.
[22]S. Y. Wu, Linear programming in measure spaces, Ph. D. Dissertation, Cambridge University, 1985.
[23]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.
[24]S. Y.Wu and C. F.Wen, An approximation approach for linear programming in measure space, Optimization and control with applications, pp. 331-350, Appl. Optim., 96, Springer, New York, 2005.
[25]M. Yamasaki, On a capacitability problem raised in connection with linear programming, Journal of Science, Hiroshima University Series A-I, Vol. 30, pp. 227-244, 1966.