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On subdifferential calculus ∗
"... The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible endgoal, the KarushKuhnTucker theorem, which is one of the main results of nonlinear programm ..."
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The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible endgoal, the KarushKuhnTucker theorem, which is one of the main results of nonlinear
Elements of quasiconvex subdifferential calculus
 J. Convex Anal
"... A number of rules for the calculus of subdifferentials of generalized convex functions are displayed. The subdifferentials we use are among the most significant for this class of functions, in particular for quasiconvex functions: we treat the GreenbergPierskalla’s subdifferential and its relatives ..."
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A number of rules for the calculus of subdifferentials of generalized convex functions are displayed. The subdifferentials we use are among the most significant for this class of functions, in particular for quasiconvex functions: we treat the GreenbergPierskalla’s subdifferential and its
Abstract subdifferential calculus and semiconvex functions
 Serdica Math. J
, 1997
"... Abstract. We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function. 1. Introduction. Throughout this paper ..."
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Abstract. We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function. 1. Introduction. Throughout this paper
A Survey of Subdifferential Calculus with Applications
 TMA
, 1998
"... This survey is an account of the current status of subdifferential research. It is intended to serve as an entry point for researchers and graduate students in a wide variety of pure and applied analysis areas who might profitably use subdifferentials as tools. ..."
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Cited by 24 (6 self)
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This survey is an account of the current status of subdifferential research. It is intended to serve as an entry point for researchers and graduate students in a wide variety of pure and applied analysis areas who might profitably use subdifferentials as tools.
METRIC INEQUALITY, SUBDIFFERENTIAL CALCULUS AND APPLICATIONS
, 2000
"... In this paper, we establish characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae. Then we establish chain rules for the limiting Fréchet subdifferentials. Necessary conditions for constrained optimization problems with nonLipschitz dat ..."
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Cited by 15 (3 self)
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In this paper, we establish characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae. Then we establish chain rules for the limiting Fréchet subdifferentials. Necessary conditions for constrained optimization problems with non
On Nonconvex Subdifferential Calculus in Banach Spaces
, 1995
"... this paper we establish some useful calculus rules in the general Banach space setting. ..."
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Cited by 4 (0 self)
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this paper we establish some useful calculus rules in the general Banach space setting.
Subdifferential Calculus Without Qualification Assumptions
 Journal of Convex Analysis
, 1996
"... this paper, L. Thibault has kindly informed us that a related condition appears in [2] and [3] in the Hilbertian case, where it is obtained with quite different methods. Again, our three conditions are more precise when X is reflexive, so that one uses sequences : the conditions ..."
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Cited by 5 (2 self)
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this paper, L. Thibault has kindly informed us that a related condition appears in [2] and [3] in the Hilbertian case, where it is obtained with quite different methods. Again, our three conditions are more precise when X is reflexive, so that one uses sequences : the conditions
On Nonconvex Subdifferential Calculus in Binormed Spaces
"... We give in this paper some useful calculus results related to the limiting subdifferential in binormed spaces (generalized limiting subdifferential) which is a generalization of the limiting subdifferential in Banach spaces [5, 6]. ..."
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We give in this paper some useful calculus results related to the limiting subdifferential in binormed spaces (generalized limiting subdifferential) which is a generalization of the limiting subdifferential in Banach spaces [5, 6].
DIRECTIONALLY LIPSCHITZIAI \ FUNCTIONS AND SUBDIFFERENTIAL CALCULUS
"... The theory of subgradients of conyex functions is r€cognized for its many apllications to optimiza,tid and diflerential equations (for examlrle, Eamiltonian systems, monotone operators). I. H. Clarke has extended the theory to non convex functions that are merety lower semicontinuous and used it to ..."
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The theory of subgradients of conyex functions is r€cognized for its many apllications to optimiza,tid and diflerential equations (for examlrle, Eamiltonian systems, monotone operators). I. H. Clarke has extended the theory to non convex functions that are merety lower semicontinuous and used it to de ve necessary conditioDs fol nonsmooth, non convex problems in optimal coltrol and mathematical programming. tr'or loca,llv Lilschitzian functions, he has proved a number of rr cs for subgradient calculation that generalize the on€s preriously kno\ar for co[vex frurctions. This paper extends snch nrles to non,convex functioru that are not necessarily locally Lipschitzia,n. Tie two main olerations con_sidered are the addition of functions a,nd the composition of a function with a. difiercntiabie mapphg. The theorems are strong enough to cover the main results howr in dhe convex case. I. Introaluction Let E he a, linei,r topological space (rvith a, iocillly convex Hausdorff topology), and let _l be an ext€ndedrealvalued fnnction on,. At each point s wherc I is 6nite, there is a weak*,closed convex (possibly empty) subset a/(c) of the dual spa,ce,4 * Fhose elements axe called subgrad,ienr,. (ot generalized fa,Cients) of I at r. ff/is convex, al(l') consists of all z € r * sucl that (1.1) flx')>.f (s)+(s'r,z> tot all s ' e E, or, in otler words, (r.2) AJ @ = {zl I <., z> \as z as a global minimum point}. Ihis is tho case for vhich the notion of subgradient vas origina,lly developed. Rockafellar llll gave the defnition for,&: Rn and proyed a oumbe! of nrles for calculaU4 al(c) whenl is expessed in terms ol otter fr]nctiom. In particllax, he shoyed that
Results 1  10
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