This paper deals with a parametric family of convexsemi-infinite optimization problems for which linear perturbations of the objective function and continuous perturbations of the right-hand side of the constraint sy...
详细信息
This paper deals with a parametric family of convexsemi-infinite optimization problems for which linear perturbations of the objective function and continuous perturbations of the right-hand side of the constraint system are allowed. In this context, Canvas et al. (SIAM J. Optim. 18:717-732, [2007]) introduced a sufficient condition (called ENC in the present paper) for the strong Lipschitz stability of the optimal set mapping. Now, we show that ENC also entails high stability for the minimal subsets of indices involved in the KKT conditions, yielding a nice behavior not only for the optimal set mapping, but also for its inverse. Roughly speaking, points near optimal solutions are optimal for proximal parameters. In particular, this fact leads us to a remarkable simplification of a certain expression for the (metric) regularity modulus given in Canovas et al. (J. Glob. Optim. 41:1-13, [2008]) (and based on Ioffe (Usp. Mat. Nauk 55(3):103-162, [2000];Control Cybern. 32:543-554, [2003])), which provides a key step in further research oriented to find more computable expressions of this regularity modulus.
A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is considered. In this method a multi-step proximal regularization is coupled with an adaptive discretization ...
详细信息
A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is considered. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. Termination of the proximal iterations at each discretization level is controlled by means of estimates, characterizing the efficiency of these iterations. A special deleting rule permits to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convex C-1-functions are studied as well as some numerical experiments are presented.
A pair of constraint qualifications in convex semi-infinite programming, namely the locally Farkas-Minkowski constraint qualification and generalized Slater constraint qualification, are studied in the paper. We analy...
详细信息
A pair of constraint qualifications in convex semi-infinite programming, namely the locally Farkas-Minkowski constraint qualification and generalized Slater constraint qualification, are studied in the paper. We analyze the relationship between them, as well as the behavior of the so-called active and sup-active mappings, accounting for the tightness of the constraint system at each point of the variables space. The generalized Slater constraint qualification guarantees a regular behavior of the supremum function (defined as supremum of the infinitely many functions involved in the constraint system), giving rise to the well-known Valadier formula.
One of the major computational bottlenecks of using the conventional cutting plane approach to solve convexprogramming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinea...
详细信息
One of the major computational bottlenecks of using the conventional cutting plane approach to solve convexprogramming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinear and nonconvex program. This paper presents a relaxed scheme to generate a new cut. In each iteration, the proposed scheme chooses a point at which the constraints are violated to a degree rather than at which the violation is maximized. A convergence proof is provided. The proposed scheme also exhibits the capability of generating an approximate solution to any level of accuracy in a finite number of iterations. (C) 1999 Elsevier Science Ltd. All rights reserved.
The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs.
The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs.
暂无评论