In this paper a survey and refinement of its recent results in the discrete optimal control theory are presented. The step control problem depending on a parameter is investigated. No smoothness of the cost function is assumed and new versions of the discrete maximum principle for the step control problem are derived Citationsubmited to the … Read more
It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper, a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly … Read more
Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. ArticleDownload View PDF
We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model of the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle … Read more
In this paper a new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can … Read more
The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. … Read more
This note presents an application of the smooth optimization technique of Nesterov for solving two-stage stochastic linear programs. It is shown that the original O(1/e) bound of Nesterov on the number of main iterations required to obtain an e-optimal solution is retained. CitationTechnical Report, School of Industrial & Systems Engineering, Georgia Institute of Technology, 2006.ArticleDownload … Read more
Different stationarity and regularity concepts for extended real-valued functions on metric spaces are considered in the paper. The properties are characterized in terms of certain local constants. A classification scheme for stationarity/regularity constants and corresponding concepts is proposed. The relations between different constants are established. CitationUniversity of Ballarat, School of Information Technology and Mathematical Sciences, … Read more
We describe a conic interior point decomposition approach for solving a large scale semidefinite programs (SDP) whose primal feasible set is bounded. The idea is to solve such an SDP using existing primal-dual interior point methods, in an iterative fashion between a {\em master problem} and a {\em subproblem}. In our case, the master problem … Read more
In this paper, we propose an interior-point method for large sparse minimax optimization. After a short introduction, where various barrier terms are discussed, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results … Read more