Applications of the Fréchet subdifferential

Durea, M.

Displaying similar documents to “Applications of the Fréchet subdifferential”

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

Ioffe, Alexander, Penot, Jean-Paul (1996)

Serdica Mathematical Journal

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The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives...

Local cone approximations in optimization

M. Castellani, M. Pappalardo (2007)

Control and Cybernetics

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Weak sharp minima in multiobjective optimization

Marcin Studniarski (2007)

Control and Cybernetics

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Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

Gadhi, N. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Aboussoror, Abdelmalek, Loridan, Pierre (1995)

Serdica Mathematical Journal

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We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present...

High order inverse function theorems

H. Frankowska (1989)

Annales de l'I.H.P. Analyse non linéaire

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A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

Deville, Robert (1995)

Serdica Mathematical Journal

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We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive...

Paraconvex analysis

Stefan Rolewicz (2005)

Control and Cybernetics

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Weak $ψ$ -sharp minima in vector optimization problems.

Xu, S., Li, S.J. (2010)

Fixed Point Theory and Applications [electronic only]

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Abstract Subdifferential Calculus and Semi-Convex Functions

Ivanov, Milen, Zlateva, Nadia (1997)

Serdica Mathematical Journal

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∗ The work is partially supported by NSFR Grant No MM 409/94. 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.