Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians.
Characterizations of the Solution Sets of Generalized Convex Minimization Problems
2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.
Characterizations of ɛ-duality gap statements for constrained optimization problems
In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.
Clarke critical values of subanalytic Lipschitz continuous functions
The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.
Coerciveness property for a class of non-smooth functionals.
Coercivity of set-valued mappings on metric spaces.
Coercivity properties for order nonsmooth functionals.
Compactly epi-Lipschitzian convex sets and functions in normed spaces.
Compensated convexity and its applications
Complément de Schur et sous-différentiel du second ordre d'une fonction convexe.
Complements, approximations, smoothings and invariance properties.
Composite semi-infinite optimization
Critical point theorems for nonlinear dynamical systems and their applications.
Decrease of C1,1 property in vector optimization
In the paper we generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of ℓ-stability for vector functions.
Delay perturbed evolution problems involving time dependent subdifferential operators
We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.
Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz...
Derivatives of Hadamard type in scalar constrained optimization
Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.
Direct design of robustly asymptotically stabilizing hybrid feedback
A direct construction of a stabilizing hybrid feedback that is robust to general measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set.
Discretization methods for nonconvex differential inclusions.
Efficiency and Duality in Nonsmooth Multiobjective Fractional Programming Involving η-pseudolinear Functions