Mathematical programs with a two-dimensional reverse convex constraint (Q1186268)

The authors consider the problem of minimizing a function \(f(x)\) subject to constraints \(x\in G\) and \(T(x)\not\in D\) with \(D\) being a closed convex set in \(\mathbb{R}^ 2\). The constraint \(T(x)\not\in D\) is a reverse convex constraint, so the feasible domain can be disconnected even when \(T\) is affine and \(G\) is a polytope. The authors show that this problem can be reduced to a quasiconcave minimization problem over a compact convex set in \(\mathbb{R}^ 2\) and hence can be solved effectively provided \(f\), \(T\) are convex and \(G\) is convex or discrete. The authors compare their approach with the parametric approach.