In this paper we investigate how to efficiently apply Approximate-Karush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model … Read more
We discuss the $l_2$-$l_p$ (with $p\in (0,1)$ matrix minimization for recovering low rank matrix. A smoothing approach is developed for solving this non-smooth, non-Lipschitz and non-convex optimization problem, in which the smoothing parameter is used as a variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any … Read more
We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Un- like monotone case, in pseudomonotone case, the regularized subprob- lems may not be strongly monotone, even not pseudomonotone. How- ever, every proximal trajectory weakly converges to the same limit, We use these properties to extend … Read more
We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-Objective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation … Read more
Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank’s trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks … Read more
In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then provide an explicit quantitative sensitivity analysis on how the solution under the robustification depends … Read more
We extend and characterize the concept of $s$-semigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in low-rank semidefinite matrix recovery. We show that s-semigoodness is not only a necessary and sufficient condition for exact $s$-rank semidefinite matrix recovery by a … Read more
This paper presents a two-step optimization approach to solve the complex scheduling problem in a job shop environment. This problem is also known as the Job Shop Scheduling Problem (JSSP). The JSSP is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. The proposed approach … Read more
The general Art Gallery Problem (AGP) consists in finding the minimum number of guards sufficient to ensure the visibility coverage of an art gallery represented by a polygon. The AGP is a well known NP-hard problem and, for this reason, all algorithms proposed so far to solve it are unable to guarantee optimality except in … Read more
We introduce a class of incremental network design problems focused on investigating the optimal choice and timing of network expansions. We concentrate on an incremental network design problem with shortest paths. We investigate structural properties of optimal solutions, we show that the simplest variant is NP-hard, we analyze the worst-case performance of natural greedy heuristics, … Read more