A globally convergent method for semi-infinite linear programming

Journal of Global Optimization - Tập 8 - Trang 189-199 - 1996
H. Hu1
1Department of Mathematical Sciences, Northern Illinois University, DeKalb, U.S.A.

Tóm tắt

This paper presents a globally convergent method for solving a general semi-infinite linear programming problem. Some important features of this method include: It can solve a semi-infinite linear program having an unbounded feasible region. It requires an inexact solution to a nonlinear subproblem at each iteration. It allows unbounded index sets and nondifferentiable constraints. The amount of work at each iteration k does not increase with k.

Tài liệu tham khảo

Bazaraa, M.S., Sherali, H.D., and Shetty, C.M. (1993), Nonlinear Programming Theory and Algorithms, John Wiley & Sons, New York. Ferris, M.C. and Philpott, A.B. (1989), An Interior Point Algorithm for Semi-infinite Linear Programming, Mathematical Programming 43, 257–276. Fletcher, R. (1981), A Nonlinear Programming Problem in Statistics (Educational Testing), SIAM Journal on Scientific and Statistical Computing 2, 257–267. Gustafson, S.-A. (1983), A Three Phase Algorithm for Semi-infinite Programs, in Fiacoo, A. V. and Kortanek, K. O. ed., Semi-infinite Programming and Applications, 138–157. Hettich, R. and Kortanek, K.O. (1993), Semi-infinite Programming: Theory, Methods, and Applications, SIAM Review 35, 380–429. Hu, H. (1990), A One-phase Algorithm for Semi-infinite Linear Programming, Mathematical Programming 46, 85–103. Hu, H. and Wang, Q. (1989), On Approximate Solutions of Infinite Systems of Linear Inequalities, Linear Algebra and its Applications 114/115, 429–438. Kortanek, K.O. and No, H. (1993), A Central Cutting Plane Algorithm for Convex Semi-infinite Programming Problems, SIAM J. Optimization 3, 901–918. Smith, B.T., Boyle, J.M., Klema, V.C., and Moler, C.B. (1970), Matrix Eigensystem Routines Guide, Springer-Verlag, Berlin. Todd, M.J. (1994), Interior-point algorithms for semi-infinite programming, Mathematical Programming 65, 217–245.