相关论文: Coderivatives with respect to a set of the normal …
This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper…
Circuits play a fundamental role in polyhedral theory and linear programming. For instance, circuits are used as step directions in various augmentation schemes for solving linear programs or to leave degenerate vertices while running the…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We start from a parametrized system of $d$ generalized polynomial equations (with real exponents) for $d$ positive variables, involving $n$ generalized monomials with $n$ positive parameters. Existence and uniqueness of a solution for all…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
A combinatorial optimization problem (COP) has a finite groundset $E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family $T\in E$ of feasible subsets with objective to find $t\in T$ with maximal weight:…
In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
We study the regularity of solutions of the Poisson equation with Dirichlet, Neumann and mixed boundary values in polyhedral cones $K\subset \mathbb{R}^3$ in the specific scale $\ B^{\alpha}_{\tau,\tau}, \…
We consider systems of strict multivariate polynomial inequalities over the reals. All polynomial coefficients are parameters ranging over the reals, where for each coefficient we prescribe its sign. We are interested in the existence of…
This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming (SOCP) at a locally optimal solution. We achieve this…
Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to…
An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…
In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps…
In this paper, the concept of coderivatives at infinity of set-valued mappings is introduced. Well-posedness properties at infinity of set-valued mappings as well as Mordukhovich's criterion at infinity are established. Fermat's rule at…
Asymmetric vector norms are generalizations of asymmetric norms, where the subadditivity inequality is understood in ordered vector space sense. This relation imposes strong conditions on the ordering itself. This note studies on these…
In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…