On the Performance of SQP Methods for Nonlinear Optimization

This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are given … Read more

Submodular Minimization in the Context of Modern LP and MILP Methods and Solvers

We consider the application of mixed-integer linear programming (MILP) solvers to the minimization of submodular functions. We evaluate common large-scale linear-programming (LP) techniques (e.g., column generation, row generation, dual stabilization) for solving a LP reformulation of the submodular minimization (SM) problem. We present heuristics based on the LP framework and a MILP solver. We evaluated … Read more

Minimizing Risk Exposure when the Choice of a Risk Measure is Ambiguous

Since the financial crisis of 2007-2009, there has been a renewed interest toward quantifying more appropriately the risks involved in financial positions. Popular risk measures such as variance and value-at-risk have been found inadequate as we now give more importance to properties such as monotonicity, convexity, translation invariance, scale invariance, and law invariance. Unfortunately, the … Read more

Metric subregularity of composition set-valued mappings with applications to fixed point theory

In this paper we underline the importance of the parametric subregularity property of set-valued mappings, defined with respect to fixed sets. We show that this property appears naturally for some very simple mappings which play an important role in the theory of metric regularity. We prove a result concerning the preservation of metric subregularity at … Read more

Hybrid Constructive Heuristics for the Critical Node Problem

We consider the Critical Node Problem: given an undirected graph and an integer number K, at most K nodes have to be deleted from the graph in order to minimize a connectivity measure in the residual graph. We combine the basic steps used in common greedy algorithms with some flavour of local search, in order … Read more

A note on the ergodic convergence of symmetric alternating proximal gradient method

We consider the alternating proximal gradient method (APGM) proposed to solve a convex minimization model with linear constraints and separable objective function which is the sum of two functions without coupled variables. Inspired by Peaceman-Rachford splitting method (PRSM), a nature idea is to extend APGM to the symmetric alternating proximal gradient method (SAPGM), which can … Read more

A new step size rule in Yan et al.’s self-adaptive projection method

In this paper, we propose a new step size rule to accelerate Yan et al.’s self-adaptive projection method. Under the new step size strategy, the superiority of modified projection method is verified through theory to numerical experiments. Citation College of Communications Engineering, PLA University of Science and Technology, Nanjing, 210007, China 01/29/2015 Article Download View … Read more

Regret Analysis of Block Coordinate Gradient Methods for Online Convex Programming

In this paper, we propose two block coordinate gradient (BCG) methods for the online convex programming: the BCG method with the cyclic rule and the BCG method with the random rule. The proposed methods solve a low dimensional problem at each iteration, and hence they are efficient for large scale problems. For the proposed methods, … Read more

An optimization-based method for feature ranking in nonlinear regression problems

In this work we consider the feature ranking problem where, given a set of training instances, the task is to associate a score to the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to … Read more

Single-Commodity Robust Network Design with Finite and Hose Demand Sets

We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of … Read more