For the classical nonlinear program two new relaxations of the Mangasarian-Fromovitz constraint qualification are discussed and their relationship with some standard constraint qualifications is examined. In particular, we establish the equivalence of one of these constraint qualifications with the recently suggested by Andreani et al. Constant rank of the subspace component constraint qualification. As an … Read more
In this paper, we present a barrier method for solving nonlinear programming problems. It employs a Levenberg-Marquardt perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We show that the Levenberg-Marquardt perturbation is equivalent to replacing the Newton step by a cubic regularization … Read more
This paper describes a nonlinear least squares framework to solve a separable nonlinear ill-posed inverse problems that arises in blind deconvolution. It is shown that with proper constraints and well chosen regularization parameters, it is possible to obtain an objective function that is fairly well behaved and the nonlinear minimization problem can be effectively solved … Read more
In this paper, we propose a primal IP method for solving the optimal experimental design problem with a large class of smooth convex optimality criteria, including A-, D- and p th mean criterion, and establish its global convergence. We also show that the Newton direction can be computed efficiently when the size of the moment … Read more
This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of … Read more
We consider the general nonlinear programming problem with equality and inequality constraints when the variables x are confined to a compact set. We regard the Lagrange multipliers as dual variables lambda, those of the inequalities being nonnegative. For each lambda, we let phi(lambda) be the least value of the Lagrange function, which occurs at x=x(lambda), … Read more
A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the Inexact Restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only … Read more
The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed rst-order necessary optimality conditions are then derived in … Read more
The family of optimization problems with value function objectives includes the minmax programming problem and the bilevel optimization problem. In this paper, we derive necessary optimality conditions for this class of problems. The main focus is on the case where the functions involved are nonsmooth and the constraints are the very general operator constraints. CitationsubmittedArticleDownload … Read more
We present the formulation and analysis of a new sequential quadratic programming (\SQP) method for general nonlinearly constrained optimization. The method pairs a primal-dual generalized augmented Lagrangian merit function with a \emph{flexible} line search to obtain a sequence of improving estimates of the solution. This function is a primal-dual variant of the augmented Lagrangian proposed … Read more