Journal ArticleDOI
On the Minimization of Difference Functions
TLDR
Simple necessary optimality conditions are formulated for a function f of the form f–h, where g and h are nonsmooth functions and related sufficient conditions are given for local minimization and global minimization.Abstract:
Simple necessary optimality conditions are formulated for a functionf of the form f=g-h, where g andh are nonsmooth functions. Related sufficient conditions are given for local minimization and global minimization.read more
Citations
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Journal ArticleDOI
Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
TL;DR: In this paper, Pallaschke et al. developed various (exact) calculus rules for Frechet lower and upper subgradients of extended real-valued functions in real Banach spaces.
Journal ArticleDOI
Convergence of New Inertial Proximal Methods for DC Programming
TL;DR: The main theorems not only recover known convergence results in this field but also provide a theoretical basis for the development of new iterative methods.
Journal ArticleDOI
On the Subdifferentiability of the Difference of Two Functions and Local Minimization
TL;DR: In this paper, the Frechet and e-Frechet subdifferentials of the difference of two convex functions are studied and necessary and sufficient conditions for local optimality in nonconvex optimization.
Journal ArticleDOI
The directional subdifferential of the difference of two convex functions
TL;DR: A criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions is provided, which relies on a notion of approximate monotonicity for operators which is much less demanding than the usual one.
Journal ArticleDOI
Glimpses upon quasiconvex analysis
TL;DR: In this paper, Atteia et al. review various sorts of generalized convexity and raise some questions about them and stress the importance of some special subclasses of quasiconvex functions.
References
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Journal ArticleDOI
Nonsmooth sequential analysis in Asplund spaces
TL;DR: In this article, a generalized differentiation theory for nonsmooth functions and sets with nonconvex boundaries defined in Asplund spaces is developed. But the analysis is restricted to the case of sets with nonsmooted boundaries.
Journal ArticleDOI
Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
TL;DR: In this article, it was shown that several minimax principles of the Ambrosetti-Rabinowitz type remain valid for functions satisfying (H) and (PS), and may therefore be used to prove the existence of critical points other than local minima.
Book ChapterDOI
Generalized Differentiability / Duality and Optimization for Problems Dealing with Differences of Convex Functions
TL;DR: In this paper, the main known results about suuch functions from the viewpoint of analysis and optimization are surveyed, and a survey of the main features of these functions can be found.
Journal ArticleDOI
First- and second-order epi-differentiability in nonlinear programming
TL;DR: In this paper, the essential objective function, which is the sum of the given objective and the indicator of the constraints, is shown to be twice epi-differentiable at any point where the active constraints satisfy the Mangasarian-Fromovitz qualification.
Book ChapterDOI
A unified theory of first and second order conditions for extremum problems in topological vector spaces
Aharon Ben-Tal,Jochem Zowe +1 more
TL;DR: In this paper, an abstract optimization problem (P) in infinite dimensional spaces is studied and necessary conditions of first and second order sufficient conditions with or without differentiability assumptions are derived for special cases of the general problem.