Related papers: A Note on the Paper "Optimality Conditions for Vec…
In this note we show that a recent existence result on quasiequilibrium problems, which seems to improve deeply some well-known results, is not correct. We exhibit a counterexample and we furnish a generalization of a lemma about continuous…
We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…
In this paper, we consider networks with topologies described by some connected undirected graph ${\mathcal{G}}=(V, E)$ and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
A recent article of J.P. Bell, K. Huang, W. Peng and T.J. Tucker establishes an analog of the Tits alternative for semigroups of endomorphisms of the projective line. The proof involves a ping-pong argument on arithmetic height functions.…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive several second-order optimality conditions for a local and a…
Consider a mapping $f\colon X\to Y$ between two metric measure spaces. We study generalized versions of the local Lipschitz number $\mathrm{Lip} f$, as well as of the distortion number $H_f$ that is used to define quasiconformal mappings.…
Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
We prove sufficient conditions in order to obtain a sharp G\aa rding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp G\aa rding inequality for compact…
In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are…