Danique de Moor In this paper, we study nonconvex optimization problems involving sum of linear times convex (SLC) functions as well as conic constraints belonging to one of the five basic cones, that is, linear cone, second order cone, power cone, exponential cone, and semidefinite cone. By using the Reformulation Perspectification Technique, we can obtain a convex relaxation … Read more
One of the great challenges in reaching zero hunger is to secure the availability of sufficient nourishment in the worst of times such as humanitarian emergencies. Food aid operations during a humanitarian emergency are typically subject to a high level of uncertainty. In this paper, we develop a novel robust optimization model for food aid … Read more
In this paper, we propose a new global optimization approach for solving nonconvex optimization problems in which the nonconvex components are sums of products of convex functions. A broad class of nonconvex problems can be written in this way, such as concave minimization problems, difference of convex problems, and fractional optimization problems. Our approach exploits … Read more
We introduce a novel Reformulation-Perspectification Technique (RPT) to obtain convex approximations of nonconvex continuous optimization problems. RPT consists of two steps, those are, a reformulation step and a perspectification step. The reformulation step generates redundant nonconvex constraints from pairwise multiplication of the existing constraints. The perspectification step then convexifies the nonconvex components by using perspective … Read more
In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this … Read more