5

Mathematical Programming

springer

1990

46

1 - 3

85-103

Semi-infinite linear programming , generalized linear programming , convex programming- ming , linear programming , duality

براي دانلود و مشاهده مقاله به قسمت لينكهاي مرتبط مراجعه نماييد

We present an algorithm for solving a large class of semi-infinite linear programming problems.This algorithm has several advantages: it handles feasibility and optimality together; it has very weak restrictions on the constraints; it allows cuts that are not near the most violated cut; and it solves the primal and the dual problems simultaneously. We prove the convergence of this algorithm in two steps. First, we show that the algorithm can find an e-optimal solution after finitely many iterations. Then, we use this result to show that it can find an optimal solution in the limit. We also estimate how good an e-optimal solution is compared to an optimal solution and give an upper bound on the total number of iterations needed for finding an e-optimal solution under some assumptions. This algorithm is generalized to solve a class of nonlinear semi-infinite programming problems. Applications to convex programming are discussed

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