This paper presents a new practical approach to complex Chebyshev approximation by semi-infinite linear programming. The approximation problem may be general with arbitrary complex basis functions. By the new front-end technique, the associated semiinfinite linear programming problem is solved exploiting the finiteness of the related Lagrange multipliers by adapting finite–dimensional linear pr...

Finite-dimensional linear programs satisfy strong duality (SD) and have the “dual 8 pricing” (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of 9 the right-hand-side vector, there exists a dual solution that correctly “prices” the perturbation by 10 computing the exact change in the optimal objective function value. These properties may fail in 11 semi-inf...

This paper presents a new practical approach to complex quadratic programming which solves the broad class of complex approximation problems employing finitization of semi-infinite formulations. The approximation problem may be general with arbitrarily complex basis functions. By using a new technique, the associated semi-infinite quadratic programming problem can be solved taking advantage of ...

We study the problem of computing linear rank inequalities, and the related problem of computing lower bounds on the linear share complexity of access structures. We prove that if one knows a generating set for the cone of linear rank inequalities on n + 1 variables, then he can use this generating set and linear programming (or semi-infinite programming) to compute the exact linear optimal inf...