Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
Semicontinuità inferiore di funzionali integrali nel caso vettoriale e buona posizione nel calcolo delle variazioni
Sensitivity analysis for relaxed cocoercive nonlinear quasivariational inclusions.
Sensitivity analysis of a nonlinear obstacle plate problem
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9, 10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...
Sensitivity analysis of extended general variational inequalities.
Sensitivity analysis of solutions to a class of quasi-variational inequalities
We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality when both the operator and the convex are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).
Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities
Shape and topological sensitivity analysis in domains with cracks
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
Shape optimization for dynamic contact problems
The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.
Shape optimization of thermoviscoelastic contact problems
Slice convergence : stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM : COCV 9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d’Attouch-Wets est stable par une classe d’opérations classiques de l’analyse convexe, lorsque les limites des suites d’ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Slice convergence: stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM: COCV9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d'Attouch-Wets est stable par une classe d'opérations classiques de l'analyse convexe, lorsque les limites des suites d'ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Some results for an optimal control problem with a semilinear state equation
We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
Stability analysis for higher-order adjacent derivative in parametrized vector optimization.
Stability analysis for parametric vector optimization problems [Book]
Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
Stability and sensitivity analysis for optimal control problems with control-state constraints [Book]
Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and...
Stability of eigenvalues and eigenvectors of variational inequalities