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Generalized Convexity, Generalized Monotonicity and Nonsmooth

This chapter is an introduction to generalized monotone multivalued maps and their relation to generalized convex functions through subdifferential theory. In particular, it contains the characterization of various types of generalized convex functions through properties of their subdifferentials. Also, some recent results on  ...


6th International Symposium on Generalized Convexity/Monotonicity

[3] Cambini A. and L. Martein, Generalized Concavity in Multiobjective Programming, in ”Gen- eralized Convexity, Generalized Monotonicity: Recent Results”, edited by J.-P. Crouzeix,. J.-E. Martinez-Legaz and M. Volle, Nonconvex Optimization and Its Applications, vol.27,. Kluwer Academic Publishers, Dordrecht, ...


Generalized Convexity and Generalized Derivatives | SpringerLink

Abstract. This chapter is devoted to the study of nonsmooth generalized convex functions with the help of special classes of generalized derivatives. Several results are presented on the links between generalized monotonicity of the generalized derivatives and generalized convexity of the functions under discussion.


Generalized Monotone Maps and Complementarity Problems

Abstract In this chapter, we present some classes of generalized monotone maps and their relationship with the corresponding concepts of generalized convexity. We present results of generalized monotone maps that are used in the analysis and solution of variational inequality and complementarity problems. In addi-.



In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, ... pings. Further, they related them to previously introduced classes of (generalized) monotonicity. Yang et al. [16] studied generalized invariant monotonicity and its .... a larger class of nonconvex optimization problems than other generalized convexity.


A Relaxed-Projection Splitting Algorithm for Variational Inequalities

Dec 29, 2015 ... Generalized convexity, generalized monotonicity: recent results: Nonconvex Optimization and Its Applications 27, 75–110 Kluwer Acad. Publ., Dordrecht ( 1998). [34] Lions, P.L., Mercier, B. Splitting algorithms for the sum of two nonlinear operators. SIAM Journal of. Numererical Analysis 16, 964–979 (1979).


Nonconvex Optimization and Its Applications

May 20, 2016 ... lems and vector optimization problems under various assumptions of generalized convexity. Such relationships are also studied for nonsmooth vector optimization problems as well. Some characterization of generalized univex functions using generalized monotonicity are also given in this chapter.

Mishra S.K., Wang S.Y., Lai K.K. Generalized convexity and vector optimization (Springer, 2009)(ISBN 3540856706)(297s)_MOc_.pdf

arXiv:1610.05470v2 [math.OC] 15 Mar 2017

Mar 15, 2017 ... A class of non-convex optimization problems with DC objective function is studied, where DC ... A function f : Rn → R ∪ {∞} is said to be polyhedral convex if its epigraph epif := {(x, r) ∈ Rn × R| r ... as the generalized convex hull of finitely many points vi ∈ Rn; i = 1,...,r; r ≥ 1 and finitely many directions dj ...


Multiobjective Programming under Nondifferentiable G-V-Invexity

new optimality results are more useful for some class of nonconvex nonsmooth vector optimization prob- lems than similarly optimality results established in the literature under other nondifferentiable generalized convexity hypotheses. Further, for the considered nonsmooth multiobjective programming problem, we also ...


Generalized monotonicity and generalized convexity

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 84, No. 2; pp. 361-376, FEBRUARY 1995. Generalized Monotonicity and Generalized Convexity 1. S. KOMLOSI 2. Communicated by S. Schaible. Abstract. Generalized monotonocity of bifunctions or multifunctions is a rather new concept in optimization ...


Error Bound for Conic Inequality in Hilbert Spaces

Mar 23, 2014 ... [4] A. S. Lewis and J. S. Pang, “Error bounds for convex inequality systems,” in Generalized Convexity, Generalized Monotonicity: Recent Results, J. P. Crouzeix , J. E. Martinez-Legaz, and M. Volle,. Eds., vol. 27 of Nonconvex Optimization and Its Applications, pp. 75–110, Kluwer Academic Publishers, ...


The system of generalized vector equilibrium problems with

the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems ... Key words: Vector equilibrium problem, Vector variational inequality, Vector optimization problem, ...... editors, Generalized Convexity, Generalized Monotonicity: Recent Results, pp. 257–275 ...


PDF (136 K)

Dec 15, 2015 ... Some existence results for generalized vector quasi-equilibrium problems . Author(s): . R. Ahmad and M. ... the concept of escaping sequences and without convexity assumptions, we prove some ..... in Nonconvex Optimization and its Applications, 38, Edited by F. Giannessi, Kluwer. Academic Publishers ...


Duality for almost convex optimization problems via the perturbation

Generalized convex functions are those non-convex functions which possess ... so-called almost convex functions: those functions whose epigraphs are almost convex sets. We show first how standard results from the convex analysis may ...... convex Optimization and and its Applications 76, Springer-Verlag, New. York, pp.


Curriculum Vitae

Jan 15, 2017 ... Monica Bianchi, Gábor Kassay and Rita Pini: An inverse map result and some applications to sensitivity of ... Gábor Kassay, Cornel Pintea and Szilárd László: Monotone operators and first category sets,. Positivity 16 ... R. I. Boţ, G. Kassay and G. Wanka: Strong Duality for Generalized Convex Optimization.

CV-Kassay Gabor-en.pdf

Statistical Models for Global Optimization

Sep 8, 2016 ... Characterizations of Generalized Convexity and Generalized Monotonicity, A Survey. In J.-P. Crouzeix, J.-E. Martinez-Legaz, and M. Volle, editors, Generalized Convexity, Generalized Monotonicity: Recent Results, volume 27 of Nonconvex Optimization and Its Applications, pages 237–256. Springer, 1998.


On nonsmooth V-invexity and vector variational-like inequalities in

Keywords Michel–Penot subdifferential · Generalized convexity ·. Nonsmooth optimization · Efficient solution · Vector variational inequalities ... In this section, we give some preliminary definitions and results, which will be used in the sequel . Let X be a real Banach space endowed with a norm · and X. ∗ its dual space with.


CURRICULUM VITAE Vicente Novo 1. Personal Data 2. Academic

Sep 7, 2017 ... Generalized Convexity and Generalized Monotonicity. Nonsmooth ... 7. Efficient and weak efficient points in vector optimization with generalized cone convexity. Applied Mathematics Letters 16, 2 (2003), 221-225 (with. M. Adán). 8. .... An overview of second order tangent sets and their application in vector.


Stochastic Mirror Descent for Non-Convex Optimization

This result contributes to the landscape of non-convex stochastic optimization by clarifying that neither ... The stochastic mirror descent (SMD) method and its variants[1, 7, 8] is arguably one of the most widely used family .... ence is a weaker and more general notion than convexity and/or operator monotonicity. In fact, as we.


On the subdifferentiability of the difference of two functions and local

Oct 10, 2009 ... The interest in the theory of nonsmooth d.c. (difference of convex) optimization problems has ... therein. Such an interest is explained by the fact that this class of functions is large: by a result of Hartman [12] .... [33] and its generalization presented in [34]; we recall these notions and present some properties.