Adaptive discretization-based algorithms for semi-infinite programs with unbounded variables

The proof of convergence of adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets for the upper- and lower-level variables. This assumption is violated in some applications, and we show that indeed convergence problems can arise when discretization-based algorithms are applied to SIPs with unbounded variables. To mitigate these convergence problems, … Read more

Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints

Discretization-based algorithms are proposed for the global solution of mixed-integer nonlinear generalized semi-infinite (GSIP) and bilevel (BLP) programs with lower-level equality constraints coupling the lower and upper level. The algorithms are extensions, respectively, of the algorithm proposed by Mitsos and Tsoukalas (J Glob Optim 61(1):1–17, 2015. and by Mitsos (J Glob Optim 47(4):557–582, 2010. … Read more

A Hybrid Discretization Algorithm with Guaranteed Feasibility for the Global Solution of Semi-Infinite Programs

A discretization-based algorithm for the global solution of semi-infinite programs (SIPs) is proposed, which is guaranteed to converge to a feasible, ε-optimal solution finitely under mild assumptions. The algorithm is based on the hybridization of two existing algorithms. The first algorithm (Mitsos in Optimization 60(10–11):1291–1308, 2011) is based on a restriction of the right-hand side … Read more