A Parallel Quadratic Programming Method for Dynamic Optimization Problems

Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details … Read more

Efficient upper and lower bounds for global mixed-integer optimal control

We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete feasible set for the controls taking into account the electrical … Read more

An inexact proximal path-following algorithm for constrained convex minimization

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment … Read more

Variational analysis in psychological modeling

This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay dynamics … Read more

Dynamic Cost Allocation for Economic Lot Sizing Games

We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this … Read more

Singularly Perturbed Markov Decision Processes: A Multiresolution Algorithm

Singular perturbation techniques allow the derivation of an aggregate model whose solution is asymptotically optimal for Markov Decision Processes with strong and weak interactions. We develop an algorithm that takes advantage of the asymptotic optimality of the aggregate model in order to compute the solution of the original model with theoretically better complexity than conventional … Read more

A First-Order Algorithm for the A-Optimal Experimental Design Problem: A Mathematical Programming Approach

We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality conditions are given. Then, two first-order (Frank-Wolfe type) algorithms are presented, accompanied by a detailed time-complexity analysis of the … Read more

An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex

The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems — it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a polynomial-time approximation scheme (PTAS) for polynomials of fixed degree, which is based on polynomial evaluations … Read more