A disadvantage of the SDP (semidefinite programming) relaxation method for quadratic
and/or combinatorial optimization problems lies in its expensive computational cost. This …

Let F be a compact subset of the n-dimensional Euclidean space Rn represented by (finitely
or infinitely many) quadratic inequalities. We propose two methods, one based on …

We consider the problem of global minimization of rational functions on (unconstrained
case), and on an open, connected, semi-algebraic subset of, or the (partial) closure of such …

Based on the authors' previous work which established theoretical foundations of two,
conceptual, successive convex relaxation methods, ie, the SSDP (Successive Semidefinite …

The nonconvex quadratic programming problem with continuous and/or binary variables is a
typical NP-hard optimization problem, which has a wide range of applications. This article …

Let F be a subset of the n-dimensional Euclidean space Rn represented in terms of a
compact convex subset of Rn and a set of finitely or infinitely many quadratic inequalities …

This paper discusses computational complexity of conceptual successive convex relaxation
methods proposed by Kojima and Tunçel for approximating a convex relaxation of a …

As computing resources continue to improve, global solutions for larger size quadrically
constrained optimization problems become more achievable. In this paper, we focus on …

General successive convex relaxation methods (SRCMs) can be used to compute the
convex hull of any compact set, in an Euclidean space, described by a system of quadratic …

We consider the problem of global minimization of rational functions on IRn (unconstrained
case), and on an open, connected, semi-algebraic subset of IRn, or the (partial) closure of …