The present work is the first member of a pair papers concerning decreasingly-minimal (dec-min) elements set integral vectors, where vector dec-min if its largest component as small possible, within this, next and so on. This discrete notion, along with fractional counterpart, showed up earlier in literature under various names. domain we consider an M-convex set, that is, base-polyhedron. A fu...

In this paper we provide an approximation à la Ambrosio-Tortorelli of some classical minimization problems involving the length of an unknown one-dimensional set, with an additional connectedness constraint, in dimension two. We introduce a term of new type relying on a weighted geodesic distance that forces the minimizers to be connected at the limit. We apply this approach to approximate the ...

In section 4.1 a new class of higher order (F,ρi, σj)type I functions are introduced for a vector minimization problem. Various known generalized invex functions such as type-I, second order type-I and second order (F,ρi,σj)-type I are particular cases of higher order (F, ρi, σj)-type I functions. This class of functions is used to establish higher order duality results for a nondifferentiable ...

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in general, neither rational functions nor the supremum of rational functions so that current results available for the minimization of rational functions cannot be ...

It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NP-hard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper, we prove, in esse...

Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes (non-convex, and even n...

We introduce a new stereo formulation which does not use pixel and disparity models. Many problems in vision are treated as assigning each pixel a label. Disparities are labels for stereo. Such pixel-labeling problems are naturally represented in terms of energy minimization, where the energy function has two terms: one term penalizes solutions that inconsistent with the observed data, the othe...