The Experts below are selected from a list of 9006 Experts worldwide ranked by ideXlab platform
Vera Roshchina - One of the best experts on this subject based on the ideXlab platform.
-
outer limits of Subdifferentials for min max type functions
Optimization, 2019Co-Authors: Andrew Eberhard, Vera Roshchina, Tian SangAbstract:We generalize the outer subdifferential construction suggested by Canovas, Henrion, Lopez and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang.
-
the directed and rubinov Subdifferentials of quasidifferentiable functions part ii calculus
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Robert Baier, Elza Farkhi, Vera RoshchinaAbstract:Abstract We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov Subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed Subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the Subdifferentials of Clarke, Dini, Michel–Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe’s axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.
-
the directed and rubinov Subdifferentials of quasidifferentiable functions part i definition and examples
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Robert Baier, Elza Farkhi, Vera RoshchinaAbstract:Abstract We extend the definition of the directed subdifferential, originally introduced in [R. Baier, E. Farkhi, The directed subdifferential of DC functions, in: A. Leizarowitz, B.S. Mordukhovich, I. Shafrir, A.J. Zaslavski (Eds.), Nonlinear Analysis and Optimization II: Optimization. A Conference in Celebration of Alex Ioffe’s 70th and Simeon Reich’s 60th Birthdays, June 18–24, 2008, Haifa, Israel, in: AMS Contemp. Math., vol. 513, AMS, Bar-Ilan University, 2010, pp. 27–43], for differences of convex functions (DC) to the wider class of quasidifferentiable functions. Such generalization efficiently captures differential properties of a wide class of functions including amenable and lower/upper- C k functions. While preserving the most important properties of the quasidifferential, such as exact calculus rules, the directed subdifferential lacks the major drawbacks of quasidifferential: non-uniqueness and “inflation in size” of the two convex sets representing the quasidifferential after applying calculus rules. The Rubinov subdifferential is defined as the visualization of the directed subdifferential.
-
On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions
Variational Analysis and Generalized Differentiation in Optimization and Control, 2010Co-Authors: Robert Baier, Elza Farkhi, Vera RoshchinaAbstract:The Mordukhovich subdifferential, being highly important in variational and nonsmooth analysis and optimization, often happens to be hard to calculate. We propose a method for computing the Mordukhovich subdifferential of differences of sublinear (DS) functions applying the directed subdifferential of differences of convex (DC) functions. We restrict ourselves to the two-dimensional case mainly for simplicity of the proofs and for the visualizations. The equivalence of the Mordukhovich symmetric subdifferential (the union of the corresponding subdifferential and superdifferential) to the Rubinov subdifferential (the visualization of the directed subdifferential) is established for DS functions in two dimensions. The Mordukhovich subdifferential and superdifferential are identified as parts of the Rubinov subdifferential. In addition, the Rubinov subdifferential may be constructed as the Mordukhovich one by Painleve–Kuratowski outer limits of Frechet Subdifferentials. The results are applied to the case of DC functions. Examples illustrating the obtained results are presented. 2010 Mathematics Subject Classification. Primary 49J52; Secondary 26B25, 49J50, 90C26
-
exhausters and Subdifferentials in non smooth analysis
Optimization, 2008Co-Authors: Vladimir F Demyanov, Vera RoshchinaAbstract:Non-smooth analysis manifested itself in the 1960s of the last century and is still gaining momentum developing new tools and harnesses and covering new areas of application. One of the notions of non-smooth analysis is that of the exhauster. The exhauster represents a dual construction in Nonsmooth Analysis. The relationships between upper and lower exhausters and various Subdifferentials of non-smooth functions are discussed in this article. It is shown that exhausters are closely related to other non-smooth tools, such as the Michel–Penot, Clarke, Gâteaux and Frechet Subdifferentials. Formulae for computing these Subdifferentials by means of exhausters are obtained. The discovered relations are all in the form of equalities, i.e. a calculus for computing the mentioned Subdifferentials by means of exhausters is provided.
Yiran He - One of the best experts on this subject based on the ideXlab platform.
-
Subdifferentials of a perturbed minimal time function in normed spaces
Optimization Letters, 2014Co-Authors: Yongle Zhang, Yiran He, Yi JiangAbstract:In a general normed vector space, we study the perturbed minimal time function determined by a bounded closed convex set \(U\) and a proper lower semicontinuous function \(f(\cdot )\). In particular, we show that the Frechet subdifferential and proximal subdifferential of a perturbed minimal time function are representable by virtue of corresponding subdifferential of \(f(\cdot )\) and level sets of the support function of \(U\). Some known results is a special case of these results.
-
Subdifferentials of a minimal time function in normed spaces
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Yi Jiang, Yiran HeAbstract:Abstract In a general normed vector space, we study the minimal time function determined by a differential inclusion where the set-valued mapping involved has constant values of a bounded closed convex set U and by a closed target set S. We show that proximal and Frechet Subdifferentials of a minimal time function are representable by virtue of corresponding normal cones of sublevel sets of the function and level or suplevel sets of the support function of U. The known results in the literature require the set U to have the origin as an interior point or U be compact. (In particular, if the set U is the unit closed ball, the results obtained reduce to the subdifferential of the distance function defined by S.)
Lionel Thibault - One of the best experts on this subject based on the ideXlab platform.
-
well posedness and Subdifferentials of optimal value and infimal convolution
Set-valued and Variational Analysis, 2019Co-Authors: Grigorii E Ivanov, Lionel ThibaultAbstract:We show that well-posedness (namely approximative well-posedness) properties of optimization problems are very efficient tools in subdifferential calculus of optimal value (marginal) function and in particular of infimal convolution. Under well-posedness conditions we establish an inclusion for the Mordukhovich limiting subdifferential of the marginal function and obtain new properties and descriptions of the Frechet, proximal and Mordukhovich limiting Subdifferentials of the infimal convolution. We also formulate sufficient conditions for well-posedness properties under consideration.
-
Subdifferential representation formula and subdifferential criteria for the behavior of nonsmooth functions
Nonlinear Analysis-theory Methods & Applications, 2006Co-Authors: Rafael Correa, Pedro Gajardo, Lionel ThibaultAbstract:Abstract Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be equivalent to certain appropriate conditions in terms of the Clarke subdifferential. The paper provides a systematic study showing that any such condition with the Clarke subdifferential is valid if and only if it holds with any operator representing the Clarke subdifferential like in the subdifferential proximal formula.
-
Integrability of Subdifferentials of directionally Lipschitz functions
Proceedings of the American Mathematical Society, 2005Co-Authors: Lionel Thibault, Nadia ZlatevaAbstract:Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of Subdifferentials of such functions over arbitrary Banach space.
-
enlarged inclusion of Subdifferentials
Canadian Mathematical Bulletin, 2005Co-Authors: Lionel Thibault, Dariusz ZagrodnyAbstract:This paper studies the integration of inclusion of Subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f included in the gamma-enlargement of the subdifferential of g, then the difference of those functions is gamma-Lipschitz over their effective domain.
-
integration of e fenchel Subdifferentials and maximal cyclic monotonicity
Journal of Global Optimization, 2005Co-Authors: Sylvie Marcellin, Lionel ThibaultAbstract:This paper concerns the integration of ?-Fenchel Subdifferentials of proper lower semicontinuous convex functions defined on arbitrary topological vector spaces. We make use of integration tools to provide a representation formula of the approximate subdifferential of convex functions, and also to identify the class of maximal cyclically monotone families of operators.
Yi Jiang - One of the best experts on this subject based on the ideXlab platform.
-
Subdifferentials of a perturbed minimal time function in normed spaces
Optimization Letters, 2014Co-Authors: Yongle Zhang, Yiran He, Yi JiangAbstract:In a general normed vector space, we study the perturbed minimal time function determined by a bounded closed convex set \(U\) and a proper lower semicontinuous function \(f(\cdot )\). In particular, we show that the Frechet subdifferential and proximal subdifferential of a perturbed minimal time function are representable by virtue of corresponding subdifferential of \(f(\cdot )\) and level sets of the support function of \(U\). Some known results is a special case of these results.
-
Subdifferentials of a minimal time function in normed spaces
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Yi Jiang, Yiran HeAbstract:Abstract In a general normed vector space, we study the minimal time function determined by a differential inclusion where the set-valued mapping involved has constant values of a bounded closed convex set U and by a closed target set S. We show that proximal and Frechet Subdifferentials of a minimal time function are representable by virtue of corresponding normal cones of sublevel sets of the function and level or suplevel sets of the support function of U. The known results in the literature require the set U to have the origin as an interior point or U be compact. (In particular, if the set U is the unit closed ball, the results obtained reduce to the subdifferential of the distance function defined by S.)
Ider Tseveendorj - One of the best experts on this subject based on the ideXlab platform.
-
generalized Subdifferentials of the sign change counting function
Journal of Global Optimization, 2016Co-Authors: Dominique Fortin, Ider TseveendorjAbstract:The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for this sign change counting function is given where classical Subdifferentials remain intractable. An attempt to prove global optimality at some point, for the 4-dimensional first non trivial example, is made by using a sufficient condition specially tailored among all the cases for this subdifferential.
-
generalized Subdifferentials of the sign change counting function
arXiv: Optimization and Control, 2013Co-Authors: Dominique Fortin, Ider TseveendorjAbstract:The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for the sign change counting function is given where classical Subdifferentials remain intractable. An attempt to prove global optimality at some point, for the 4-dimensional first non trivial example, is made by using a sufficient condition specially tailored among all the cases for this subdifferential.
