Results 41 to 50 of about 2,308 (150)
Separable determination of integrability and minimality of the Clarke subdifferential mapping [PDF]
Proceedings of the American Mathematical Society, 1999 In this paper we show that the study of integrability and D D -representability of Lipschitz functions defined on arbitrary
Borwein, Jonathan M., Moors, Warren B.
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KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization [PDF]
, 2014 For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question.
Dempe, Stephan, Zemkoho, Alain B.
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Nonlinear Analysis, 2019 In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition.
Yatian Pei, Yong-Kui Chang
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Optimizing condition numbers [PDF]
, 2009 In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function.
Jane J. Ye, Lewis A.S., Pierre Maréchal
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Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure [PDF]
, 2013 We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the DC structure of the function.
Baier, Robert +2 more
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On the Clarke subdifferential of the distance function of a closed set
Journal of Mathematical Analysis and Applications, 1992 The authors derive formulas for computing the Clarke subdifferential of the distance function \(x\in X\mapsto d_ C(x)=\text{Inf}\{\| x- y\|: y\in C\}\). In connection with this question, they examine the role of the dimensionality of \(X\), the convexity of \(C\), and the (subdifferential) regularity of \(d_ C\).
Burke, James V +2 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper defines a strong convertible nonconvex (SCN) function for solving the unconstrained optimization problems with the nonconvex or nonsmooth (nondifferentiable) function. First, the concept of SCN function is defined, where the SCN functions are nonconvex or nonsmooth.
Min Jiang +4 more
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Viable solutions to nonautonomous inclusions without convexity [PDF]
, 2003 The existence of viable solutions is proven for nonautonomous upper semicontinuous differential inclusions whose right-hand side is contained in the Clarke subdifferential of a locally Lipschitz continuous ...
Kánnai, Zoltán, Tallos, Péter
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Characterization of the monotone polar of subdifferentials
, 2013 We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point.
Lassonde, Marc
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Second-order subdifferential calculus with applications to tilt stability in optimization [PDF]
, 2011 The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full
Mordukhovich, B. S., Rockafellar, R. T.
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