Convergence of a Tuy-type algorithm for concave minimization subject to linear inequality constraints

Abstract

Abstract. A modification of Tuy's cone splitting algorithm for minimizing a concave function subject to linear inequality constraints is shown to be convergent by demonstrating that the limit of a sequence of constructed convex polytopes contains the feasible region. No geometric tolerance parameters are required.

Outer approximation algorithms for DC programs and beyond

“…This algorithm was shown to cycle in some cases, some algorithms were given later for detecting the cycles, see [65]. Many variants of Tuy [99] have been proposed by Bali [4], Jacobsen [54], Horst and Tuy [46], Zwart [130]. This type of algorithms performs quite well even though they are not very theoretically satisfactory [9].…”