This note establishes a limiting formula for the conic Lagrangian dual of convex infinite optimization problem, correcting classical version Karney [Math. Programming 27 (1983) 75-82] semi-infinite programs. A reformulation problem with single constraint leads to corresponding dual, called sup-dual, and also primal in case when strong Slater condition holds, which entails sup-duality.

We develop an iterative method for solving the KKT system of the semi-infinite programming (SIP) problem. At each iteration, we solve the KKT system of a nonlinear programming problem with finite constraints by a semismooth Newton method. The algorithm either terminates at a KKT point of the SIP problem in finitely many iterations or generates an infinite sequence of iterates whose any accumula...

In this paper, a truncated projected Newton-type algorithm is presented for solving large-scale semi-infinite programming problems. This is a hybrid method of a truncated projected Newton direction and a modified projected gradient direction. The truncated projected Newton method is used to solve the constrained nonlinear system. In order to guarantee global convergence, a robust loss function ...

This paper presents a new practical approach to semi-infinite complex Chebyshev approximation. By using a new technique, the general complex Chebyshev approximation problem can be solved with arbitrary base functions taking advantage of the numerical stability and efficiency of conventional linear programming software packages. Furthermore, the optimization procedure is simple to describe theor...

Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And methods use loose over-approximation of uncertainties, leading to conservative controls. To address these challenges, we propose a control-limits aware framework bounded state-de...