Hidden convexity in a class of optimization problems with bilinear terms

In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more

A universal and structured way to derive dual optimization problem formulations

The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel’s duality theorem. This alternative way of forming a strong dual problem is the subject in this paper. We recall some standard results from convex analysis and then … Read more

Robust nonlinear optimization via the dual

Robust nonlinear optimization is not as well developed as the linear case, and limited in the constraints and uncertainty sets it can handle. In this work we extend the scope of robust optimization by showing how to solve a large class of robust nonlinear optimization problems. The fascinating and appealing property of our approach is … Read more

Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets

We propose a new way to derive tractable robust counterparts of a linear program by using the theory of Beck and Ben-Tal (2009) on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new {\it convex} reformulation of the dual problem of a robust linear program, and then … Read more

Robust counterparts of inequalities containing sums of maxima of linear functions

This paper adresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter … Read more