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Nonsmooth Analysis

Nonsmooth analysis approach to Isaac's equation

Nonsmooth analysis approach to Isaac's equation

... usc at each point t,z F, then Isaacs’ equation admits exactly one solution wt,x w+t,z w_t,z, which happens to be continuous on In the lt section, we return to the differential game we st[r] ...

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Nonsmooth analysis and optimization on partially ordered vector spaces

Nonsmooth analysis and optimization on partially ordered vector spaces

... A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice.. Sample applications to the theory of nonsmoot[r] ...

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Variational methods for nonsmooth mechanics

Variational methods for nonsmooth mechanics

... methods that use a penalty formulation to regularize the problem. This approach relies on the definition of a proper gap function as a means to detect and penalize the interpene- tration; see, for example, Simo et al. ...

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Oscillating global continua of positive solutions of second order Neumann problem with a set-valued term

Oscillating global continua of positive solutions of second order Neumann problem with a set-valued term

... years, nonsmooth analysis has come to play an important role in functional analysis [1], dynamical systems [2], control theory [3], optimization [4], mechanical sys- tems [5], differential equation ...

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Higher order error bound for the difference of two functions

Higher order error bound for the difference of two functions

... The rest of this paper is organized as follows. In Sect. 2, we give some notions. In Sect. 3, we establish sufficient and necessary conditions for the existence of higher-order error bounds for difference functions with set ...

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APPROXIMATE OPTIMALITY CONDITIONS

APPROXIMATE OPTIMALITY CONDITIONS

... nonlinear analysis, in which he enjoyed a great variation of applications ranging from geometry Banach spaces see [1], in optimization theory see Ekeland [3],[4] and sub-differential generalized calculation to ...

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Minimization of nonsmooth integral functionals

Minimization of nonsmooth integral functionals

... Using concepts and techniques form nonsmooth analysis, we are able to obtain necessary and sufficient conditions for optimality in finite dimensional, convex problems see theorem 3.1 and[r] ...

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On Generalized High Order Derivatives of Nonsmooth Functions

On Generalized High Order Derivatives of Nonsmooth Functions

... In this section, we present definitions and results concerning GFD and GSD, which are needed in the remainder of this paper. In order to get this approach some tools from nonsmooth analysis are used, ...

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Nonconvex composite multiobjective nonsmooth fractional programming

Nonconvex composite multiobjective nonsmooth fractional programming

... for nonsmooth multiobjective programming problems involving locally Lipschitz ...for nonsmooth multiobjective fractional programming ...considered nonsmooth multiobjective programming problems with ...

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Optimality and duality for nonsmooth multiobjective optimization problems

Optimality and duality for nonsmooth multiobjective optimization problems

... In this paper, we consider a nonsmooth multiobjective programming problems including support functions with inequality and equality constraints. Necessary and sufficient optimality conditions are obtained by using ...

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Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

... to nonsmooth multiobjective programming problem involving support ...introduce nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions for inequality and ...

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Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization

Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization

... In this paper, we consider a class of nonsmooth multiobjective programming problems. Necessary and sufficient optimality conditions are obtained under higher order strongly convexity for Lipschitz functions. We ...

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Model reference adaptive control of a nonsmooth dynamical system

Model reference adaptive control of a nonsmooth dynamical system

... of nonsmooth dynamics typically destabilizes these controllers [10, ...a nonsmooth ‘dead zone’ characteristic and shown to give stable and robust ...

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Existence results for nonlocal and nonsmooth hemivariational inequalities

Existence results for nonlocal and nonsmooth hemivariational inequalities

... In Section 4 we recall an abstract existence result for an operator equation in ordered Banach spaces, which together with the results of Section 3 form the main tools in the proof of Th[r] ...

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Nonsmooth Optimization Algorithms in Some Problems of Fracture Dynamics

Nonsmooth Optimization Algorithms in Some Problems of Fracture Dynamics

... tions. Nonsmooth functionals that correspond to unilare- ral frictional contact conditions are constructed. Iterative algorithms of the Uzawa’s type that are based on projec- tion on the set of unilateral ...

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Duality for nonsmooth mathematical programming problems with equilibrium constraints

Duality for nonsmooth mathematical programming problems with equilibrium constraints

... In this paper, we introduce Wolfe-type and Mond-Weir-type dual programs to the non- smooth MPEC. We have established weak and strong duality theorems relating the nons- mooth MPEC and the two dual programs. The paper is ...

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A New Definition for Generalized First Derivative of Nonsmooth Functions

A New Definition for Generalized First Derivative of Nonsmooth Functions

... problem. So, by solving this problem for nonsmooth functions, we obtain an approximate derivative for these functions on interval   0,1 which is GFD. Firstly, we state the following Lemma which C   0,1 is ...

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Pseudo-transient continuation for nonsmooth nonlinear equations

Pseudo-transient continuation for nonsmooth nonlinear equations

... 1. Introduction. In this paper we show how pseudo-transient continuation (Ψtc ) can be used to solve a class of nonsmooth nonlinear equations. Ψtc is a predictor-corrector method for efficient integration of a ...

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Inertial proximal alternating minimization for nonconvex and nonsmooth problems

Inertial proximal alternating minimization for nonconvex and nonsmooth problems

... In this paper, we present a proximal alternating minimization algorithm with inertial ef- fect for the minimization problem of the type L(x, y) = f (x) + R(x, y) + g(y), where f and g are both nonconvex nonsmooth ...

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Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems

Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems

... and nonsmooth vector optimization problems in Banach ...and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued ...and nonsmooth vector optimization ...

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