In this paper, we establish a linear convergence result for the forward-backward splitting algorithm in the finding a zero of the sum of two maximal monotone operators, where one of them is set-valued strongly monotone and the other is Lipschitz continuous. We show that our convergence rate is better than Douglas–Rachford splitting algorithm’s rate used … Read more
We consider the (single-stage) stochastic bin packing problem (SBPP) which is based on a given list of items the sizes of which are represented by stochastically independent random variables. The SBPP requires to determine the minimum number of unit capacity bins needed to pack all the items, such that for each bin the probability of … Read more
Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging against a range of distributions, properly characterized in an ambiguity set, is of interest. We study two-stage stochastic programs with linear recourse in the context of distributional ambiguity, and … Read more
Logistics companies often operate a heterogeneous fleet of equipment to support their service network operations. This introduces a layer of planning complexity as facilities need to maintain appropriate levels of equipment types to support operations throughout the planning horizon. We formulate an optimization model that minimizes the cost of executing a load plan, assuming knowledge … Read more
We introduce a family of weighted conjugate-gradient-type methods, for strictly convex quadratic functions, whose parameters are determined by a minimization model based on a convex combination of the objective function and its gradient norm. This family includes the classical linear conjugate gradient method and the recently published delayed weighted gradient method as the extreme cases … Read more
Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter’s co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles … Read more
We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x – c\| \le b^T x – a$. In particular, we present a class of valid cuts that improve existing semidefinite programming (SDP) … Read more
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all guaranteed globally optimal solutions for frame and shell structures under multiple load cases and self-weight. To this purpose, we exploit the fact that the stiffness matrix is … Read more
Although many algorithms for multicriteria optimization provide good approximations, a precise control of their quality is challenging. In this paper we provide algorithmic tools to obtain exact approximation quality values for given approximations and develop a new method for multicriteria optimization guided by this quality. We show that the well-established “-indicator measure is NP-hard to … Read more
In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model … Read more