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Newton's methods for variational inclusions under conditioned Fréchet derivative

Ioannis K. Argyros, Saïd Hilout (2007)

Applicationes Mathematicae

Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.

Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics

Daniel Goeleven (1996)

Applications of Mathematics

This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications.

Nonconcentrating generalized Young functionals

Tomáš Roubíček (1997)

Commentationes Mathematicae Universitatis Carolinae

The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (= p th power) does not concentrate in the sense that it is relatively weakly compact in L 1 ( Ω ) . Straightforward applications to coercive optimization problems are briefly outlined.

Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control

Mustapha Serhani, Nadia Raïssi (2009)

RAIRO - Operations Research

In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (α), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential, we give a more...

Nonlinear dynamic systems and optimal control problems on time scales

Yunfei Peng, Xiaoling Xiang, Yang Jiang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula...

Nonlinear dynamic systems and optimal control problems on time scales*

Yunfei Peng, Xiaoling Xiang, Yang Jiang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula...

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