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Some typos in the book that we noticed are of trivial nature and do not need an explanation. There are, however, more subtle corrections that need to be made. There are also simple extensions and additions to the material presented in the book which are worthwhile to mention. 1 Corrections Section 2.1.4 In Section 2.1.4, X and X * are assumed to be paired(More)
This paper presents an overview of some recent, and significant, progress in the theory of optimization problems with perturbations. We put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems. These methods allow one to compute expansions of the optimal value function and approximate optimal(More)
In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second(More)
We present a perturbation theory for nite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. We derive Lipschitz and HH older expansions of approximate optimal solutions, under a directional constraint qualiication hypothesis and various second order suucient conditions that take into account(More)
This paper presents a second-order analysis for a simple model optimal control problem of a partial diierential equation, namely a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be minimized is a standard quadratic functional. Assuming the feasible set to be polyhedric, we state necessary and suucient second(More)
The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessen-tial) touch points, the arc structure of the trajectory is not stable. We show how to perform a sensitivity analysis that predicts which touch points will, under a small perturbation, become inactive, remain touch points(More)
We present an extension, for nonlinear optimization under linear constraints, of an algorithm for quadratic programming using a trust region idea introduced by Ye and Tse [Math. Due to the nonlinearity of the cost, we use a linesearch in order to reduce the step if necessary. We prove that, under suitable hypotheses, the algorithm converges to a point(More)
This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case.(More)