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- Subjects
- 49-XX Calculus of variations and optimal control; optimization
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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.
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.
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” (=th power) does not concentrate in the sense that it is relatively weakly compact in . Straightforward applications to coercive optimization problems are briefly outlined.
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...
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...
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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