1053-5888/10/$26.00©2010IEEE C onvex optimization has been used in signal processing for a long time to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total variation denoising, compressed sensing, fault detection, and image c...

Global optimization of mixed-integer nonlinear bilevel optimization problems is addressed using a novel technique. For problems where integer variables participate in both inner and outer problems, the outer level may involve general mixed-integer nonlinear functions. The inner level may involve functions that are mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in...

In this paper we develop a subgradient optimization methodology for convex multiparametric nonlinear programs. We define a parametric subgradient, extend some classical optimization results to the multiparametric case, and design a subgradient algorithm that is shown to converge under traditional conditions. We use this algorithm to solve two illustrative example problems and demonstrate its ac...

We propose an alternative method for computing e¤ectively the solution of the control inventory problem under non-convex polynomial cost functions. We apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. We device computational tools based on convex o...

In the eld of nonlinear programming (in continuous variables) convex analysis [21, 22] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called \discrete convex analysis" [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid theo...