An implementation of a discretization method for semi-infinite programming
Mathematical Programming: Series A and B
A note on an implementation of a method for quadratic semi-infinite programming
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
The design of FIR filters in the complex plane by convex optimization
Signal Processing
Numerical experiments in semi-infinite programming
Computational Optimization and Applications
Maple Computer Manual for Advanced Engineering Mathematics
Maple Computer Manual for Advanced Engineering Mathematics
An Adaptive Dual Parametrization Algorithm for Quadratic Semi-infinite Programming Problems
Journal of Global Optimization
An accelerated central cutting plane algorithm for linear semi-infinite programming
Mathematical Programming: Series A and B
Penalty and Smoothing Methods for Convex Semi-Infinite Programming
Mathematics of Operations Research
IEEE Transactions on Signal Processing
Computational Optimization and Applications
A new exact penalty method for semi-infinite programming problems
Journal of Computational and Applied Mathematics
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In this paper we propose a new exchange method for solving convex semi-infinite programming (CSIP) problems. We introduce a new dropping-rule in the proposed exchange algorithm, which only keeps those active constraints with positive Lagrange multipliers. Moreover, we exploit the idea of looking for $\eta$-infeasible indices of the lower level problem as the adding-rule in our algorithm. Hence the algorithm does not require to solve a maximization problem over the index set at each iteration; it only needs to find some points such that a certain computationally-easy criterion is satisfied. Under some reasonable conditions, the new adding-dropping rule guarantees that our algorithm provides an approximate optimal solution for the CSIP problem in a finite number of iterations. In the numerical experiments, we apply the proposed algorithm to solve some test problems from the literature, including some medium-sized problems from complex approximation theory and FIR filter design. We compare our algorithm with an existing central cutting plane algorithm and with the semi-infinite solver fseminf in MATLAB toolbox, and we find that our algorithm solves the CSIP problem much faster. For the FIR filter design problem, we show that our algorithm solves the problem better than some algorithms that were technically established for the problem.