In the analysis of complex stochastic dynamic programs, we often seek strong theoretical guarantees on the suboptimality of heuristic policies. One technique for obtaining performance bounds is perfect information analysis: this approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future … Read more
This paper studies the problem of multi-plant manganese alloy production. The problem consists of finding the optimal furnace feed of ores, fluxes, coke, and slag that yields output products which meet customer specifications, and to optimally decide the volume, composition, and allocation of the slag. To solve the problem, a nonlinear pooling problem formulation is … Read more
The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or … Read more
We exactly solve the NP-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit … Read more
This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a … Read more
An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to possibly non-smooth and non-convex lower semi-continuous functions that satisfy the Kurdyka–Lojasiewicz (KL) inequality, which comprises a huge class of problems. Most of … Read more
We propose and analyze two mathematical programming models for a production, inventory, distribution and routing problem considering real and relevant features from the furniture industry, such as production sequence-dependent setup times, heterogeneous fleet of vehicles, routes extending over one or more periods of the production planning horizon, multiple time windows and customers’ deadlines, among others. … Read more
In this paper, we study the strength of aggregation cuts for sign-pattern integer programs (IPs). Sign-pattern IPs are a generalization of packing IPs and are of the form {x \in Z^n | Ax = 0} where for a given column j, A_{ij} is either non-negative for all i or non-positive for all i. Our first … Read more
Many optimization algorithms converge to stationary points. When the underlying problem is nonconvex, they may get trapped at local minimizers and occasionally stagnate near saddle points. We propose the Run-and-Inspect Method, which adds an “inspect” phase to existing algorithms that helps escape from non-global stationary points. The inspection samples a set of points in a … Read more
Abstract. In the paper [9] we derived first order (KKT) and second order (SSC) optimality conditions for functions defined by evaluation programs involving smooth elementals and absolute values. In that analysis, a key assumption on the local piecewise linearization was the Linear Independence Kink Qualification (LIKQ), a generalization of the Linear Independence Constraint Qualification (LICQ) … Read more