Results 21 to 30 of about 123 (108)
Tangent cones and quasi-interiorly tangent cones to multifunctions [PDF]
, 1983 R. T. Rockafellar has proved a number of rules of subdifferential calculus for nonlocally lipschitzian real-valued functions by investigating the Clarke tangent cones to the epigraphs of such functions.
Lionel Thibault
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Characterization of the Clarke regularity of subanalytic sets [PDF]
, 2017 International audienceIn this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with ...
Abderrahim Jourani +3 more
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Proximal Analysis and Boundaries of Closed Sets in Banach Space, Part I: Theory [PDF]
, 1986 As various types of tangent cones, generalized derivatives and subgradients prove to be a useful tool in nonsmooth optimization and nonsmooth analysis, we witness a considerable interest in analysis of their properties, relations and applications ...
H. M. Strojwas, J. M. Borwein
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Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Nonnegative sparsity‐constrained optimization problem arises in many fields, such as the linear compressing sensing problem and the regularized logistic regression cost function. In this paper, we introduce a new stepsize rule and establish a gradient projection algorithm. We also obtain some convergence results under milder conditions.
Ye Li, Jun Sun, Biao Qu, Chuanjun Chen
wiley +1 more source
Chain rules for nonsmooth functions [PDF]
, 1991 A systematic method is presented for the derivation of chain rules for compositions of functions F ° f, where F is nondecreasing. This method is valid for directional derivatives and subgradients associated with any tangent cone having a short list of ...
Ward, Doug
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Jacobian Nonsingularity in Nonlinear Symmetric Conic Programming Problems and Its Application
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This paper considers the nonlinear symmetric conic programming (NSCP) problems. Firstly, a type of strong sufficient optimality condition for NSCP problems in terms of a linear‐quadratic term is introduced. Then, a sufficient condition of the nonsingularity of Clarke’s generalized Jacobian of the Karush–Kuhn–Tucker (KKT) system is demonstrated. At last,
Yun Wang, Dezhou Kong, Xinguang Zhang
wiley +1 more source
Epi-Lipschitzian reachable sets of differential inclusions [PDF]
, 2007 The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well-known assumptions of Filippov's existence theorem (about differential inclusions), every epi ...
Lorenz, Thomas
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Using EPECs to model bilevel games in restructured electricity markets with locational prices [PDF]
, 2006 CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal
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Sedimentology, Volume 73, Issue 1, Page 147-185, January 2026.ABSTRACT Mongolia's Eastern and Western Gobi Basins preserve a globally significant record of Cretaceous terrestrial vertebrates, yet their biostratigraphic correlations are complicated by a complex geological history. The Eastern Gobi Basin, a northeast‐southwest trending fault‐bounded rift system, includes several minor sub‐basins with distinct ...
Ryan T. Tucker +9 more
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Sequential Bouligand Tangent Cone and Clarke Tangent Cone in a Real Normed Space [PDF]
, 2014 In this paper, we discuss several basic properties of cone, convex, tangent cone, and bring to a focus on the sequential Bouligand tangent cone which is also called the contingent cone.
Saw Win
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