Results 21 to 30 of about 451 (54)

New Multirectional Mean Value Inequality [PDF]

arXiv, 2017
We establish new and stronger inequality of Clarke-Ledyaev type by direct construction.
arxiv  

A further improvement of a minimax theorem of Borenshtein and Shulman [PDF]

J. Nonlinear Convex Anal., 2 (2001), 279-283, 2004
I do improve a recent improvement (due to Saint Raymond) of a minimax theorem of Borenshtein and Shul'man, replacing a global compactness assumption by a local one.
arxiv  

An affirmative answer to a problem posed by Zalinescu [PDF]

arXiv, 2009
Recently, in [5] Zalinescu posed a question about the characterization of the intrinsic core of the Minkowski sum of two graphs associated with two maximal monotone operators. In this note we give an affirmative answer.
arxiv  

Generic nondegeneracy in convex optimization [PDF]

Proc. Amer. Math. Soc. 139 (2011), 2519-2527, 2010
We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally, for lower-C^2 functions.
arxiv  

First order dependence on uncertainty sets in robust optimization [PDF]

arXiv, 2010
We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem.
arxiv  

Optimality Conditions for Bilevel Programming Problem in Asplund Spaces [PDF]

arXiv, 2011
Here, necessary optimal condition for Optimistic Bilevel programming problem is obtained in Asplund spaces. Also we have got necessary optimal conditions in finite dimensional spaces, by assuming differentiability on the given functions.
arxiv  

Characterizations of Nonsmooth Robustly Quasiconvex Functions [PDF]

arXiv, 2018
Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Fr\'echet subdifferentials in Asplund spaces.
arxiv  

On a class of Variational-Hemivariational Inequalities involving set valued mappings [PDF]

Advances in Pure and Applied Mathematics, vol.1, no.2/2009, 2009
Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several sufficient conditions for the existence of solutions in the case of unbounded subsets.
arxiv  

Higher-Order Optimality Conditions in Set-Valued Optimization with Respect to General Preference Mappings. [PDF]

Set Valued Var Anal, 2022
Michalak A, Studniarski M.
europepmc   +1 more source

Semi-algebraic functions have small subdifferentials [PDF]

arXiv, 2010
We prove that the subdifferential of any semi-algebraic extended-real-valued function on $\R^n$ has $n$-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.
arxiv