Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more

Generalized Inexact Proximal Algorithms: Habit’s/ Routine’s Formation with Resistance to Change, following Worthwhile Changes

This paper shows how, in a quasi metric space, an inexact proximal algorithm with a generalized perturbation term appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,…). More precisely, the new perturbation term represents an index of resistance to change, defined as a “curved enough” function of the quasi distance … Read more

Dynamic scaling in the Mesh Adaptive Direct Search algorithm for blackbox optimization

Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer sim- ulation. The subject of this work is the Mesh Adaptive Direct Search (MADS) class of algorithms for blackbox optimization. We propose a way to dynamically scale the mesh, which is the discrete spatial structure … Read more

Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant … Read more

K-Adaptability in Two-Stage Robust Binary Programming

Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multi-stage problems with continuous recourse. This paper takes a step towards extending the robust optimization methodology to problems with integer recourse, which … Read more

On the Direct Extension of ADMM for Multi-block Separable Convex Programming and Beyond: From Variational Inequality Perspective

When the alternating direction method of multipliers (ADMM) is extended directly to a multi-block separable convex minimization model whose objective function is in form of more than two functions without coupled variables, it was recently shown that the convergence is not guaranteed. This fact urges to develop efficient algorithms that can preserve completely the numerical … Read more

Efficient combination of two lower bound functions in univariate global optimization

We propose a new method for solving univariate global optimization problems by combining a lower bound function of ®BB method (see [1]) with the lower bound function of the method developed in [4]. The new lower bound function is better than the two lower bound functions. We add the convex/concave test and pruning step which … Read more

Mathematical Programming techniques in Water Network Optimization

In this article we survey mathematical programming approaches to problems in the field of water network optimization. Predominant in the literature are two different, but related problem classes. One can be described by the notion of network design, while the other is more aptly termed by network operation. The basic underlying model in both cases … Read more

Robust optimal sizing of an hybrid energy stand-alone system

This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines, solar photovoltaic panels and batteries. To compensate for a possible lack of energy from these sources, an auxiliary fuel generator uarantees to meet the demand in every case but its use induces important costs. We have chosen a two-stage … Read more

Finding the largest low-rank clusters with Ky Fan 2-k-norm and l1-norm

We propose a convex optimization formulation with the Ky Fan 2-k-norm and l1-norm to fi nd k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under … Read more