The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program -minimize a convex function subject to inequality constraints on other convex functions. The present approach uses the support planes of the constraint region to transform the convex program into an equivalent linear program. Then the d...

In this paper, we examine the duality gap between the robust counterpart of a primal uncertain convex optimization problem and the optimistic counterpart of its uncertain Lagrangian dual and identify the classes of uncertain problems which do not have a duality gap. The absence of a duality gap (or equivalently zero duality gap) means that the primal worst value equals the dual best value. We f...

Lifts/extended formulations/cone representations of convex sets currently form an active area of research in optimization, computer science, real algebraic geometry and convex geometry. We invite high quality papers on all optimization related aspects of this topic for a special issue of Mathematical Programming, Series B. All submitted papers will be refereed according to the standards of Math...

In the conic formulation of a convex optimization problem the constraints are expressed as linear inequalities with respect to a possibly non-polyhedral convex cone. This makes it possible to formulate elegant extensions of interior-point methods for linear programming to general nonlinear convex optimization. Recent research on cone programming algorithms has particularly focused on three conv...