Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint

TL;DR

This paper develops a generalized Benders decomposition algorithm for a specific class of MINLPs with vector conic constraints in Banach spaces, extending convergence results beyond finite-dimensional cases.

Contribution

It introduces a novel algorithm for MINLPs with vector conic constraints in Banach spaces, supported by new convergence theorems that generalize existing finite-dimensional results.

Findings

Algorithm successfully solves the class of MINLPs studied.

Convergence theorems extend previous finite-dimensional results.

Deep duality theory underpins the method.

Abstract

In this paper, we mainly study one class of mixed-integer nonlinear programming problems (MINLPs) with vector conic constraint in Banach spaces. Duality theory of convex vector optimization problems applied to this class of MINLPs is deeply investigated. With the help of duality, we use the generalized Benders decomposition method to establish an algorithm for solving this MINLP. Several convergence theorems on the algorithm are also presented. The convergence theorems generalize and extend the existing results on MINLPs in finite dimension spaces.