An exact penalty on bilevel programs with linear vector optimization lower level

We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples.Bilevel programming Linear programming Multiple objective programming Penalty methods

Resistance variation of conductive ink applied by the screen printing technique on different substrates

This research study focuses on the application of conductive ink by the screen printing technique to evaluate the potential of creating printed electrodes and to investigate the effect of washing upon electrical resistance and flexibility. Two conductive inks were applied by a conventional screen printing method on four different textile substrates, 100% cotton, 50%/50% cotton/polyester, 100% polyester and 100% polyamide. The inks were also applied on a multifibre fabric. Atmospheric plasma treatment was applied to improve the adhesion to the samples, and the resistance values were compared with those of non-treated samples. The values were measured before and after cleaning and washing tests, which were performed to simulate domestic treatment for garments to predict the behaviour of the inks after normal usage of the fabrics. Comfort properties like stiffness of the fabrics were also evaluated after five and 10 washing cycles. It was observed that PE 825 ink forms a thicker film on the fabric surface, contributing to the loss of flexibility of the textile. However, PE 825 ink also produced the best results in terms of durability and lower values of resistance. Polyamide fabrics lost their conductive property after five washing cycles due to weak bonding between the ink and the fibres, whereas cotton fibres provided the best results.This work is financed by Project“Deus ex Machina”, NORTE-01-0145-FEDER-000026, funded by CCDRN, through Sistema de Apoio à Investigação Cientifica e Tecnológica (Projetos Estruturados I&D&I) of Programa Operacional Regional do Norte, from Portugal 2020 and by Project UID/CTM/00264/2019 of 2C2T –Centro de Ciência e Tecnologia Têxtil, funded by National Founds through FCT/MCTES.Derya Tama thanks FCT for fellowship 2C2T-BPD-08-2017

Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem

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, 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 method in order to approach this problem. We prove that the Hausdorff-Pompeiu distance between the weakly Pareto sets associated with the Sample Average Approximation problem and the true weakly Pareto set converges to zero almost surely as the sample size goes to infinity, assuming that our Stochastic Multi-objective Optimization Problem is strictly convex. Then we show that every cluster point of any sequence of optimal solutions of the Sample Average Approximation problems is almost surely a true optimal solution. To handle also the non-convex case, we assume that the real objective to be minimized over the Pareto set depends on the expectations of the objectives of the Stochastic Optimization Problem, i.e. we optimize over the image space of the Stochastic Optimization Problem. Then, without any convexity hypothesis, we obtain the same type of results for the Pareto sets in the image spaces. Thus we show that the sequence of optimal values of the Sample Average Approximation problems converges almost surely to the true optimal value as the sample size goes to infinity. © 2013 Springer Science+Business Media New York

Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems

We present optimality conditions for bilevel optimal control problems where the upper level is a scalar optimal control problem to be solved by a leader and the lower level is a multiobjective convex optimal control problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing amongst efficient optimal controls. We deal with the so-called optimistic case, when the followers are assumed to choose the best choice for the leader amongst their best responses, as well with the so-called pessimistic case, when the best response chosen by the followers can be the worst choice for the leader. This paper continues the research initiated in Bonnel (SIAM J. Control Optim. 50(6), 3224-3241, 2012) where existence results for these problems have been obtained. © Springer Science+Business Media New York 2013