The cone of Completely Positive (CP) matrices can be used to exactly formulate a variety of NP-Hard optimization problems. A tractable relaxation for CP matrices is provided by the cone of Doubly Nonnegative (DNN) matrices; that is, matrices that are both positive semidefinite and componentwise nonnegative. A natural problem in the optimization setting is then … Read more
Given linear matrix inequalities (LMIs) L_1 and L_2, it is natural to ask: (Q1) when does one dominate the other, that is, does L_1(X) PsD imply L_2(X) PsD? (Q2) when do they have the same solution set? Such questions can be NP-hard. This paper describes a natural relaxation of an LMI, based on substituting matrices … Read more
We present a proactive energy management framework that integrates predictive dynamic building models and day-ahead forecasts of disturbances affecting efficiency and costs. This enables an efficient management of resources and an accurate prediction of the daily electricity demand profile. The strategy is based on the on-line solution of mixed-integer nonlinear programming problems. The framework is … Read more
The multiobjective bilevel program is a sequence of two optimization problems where the upper level problem is multiobjective and the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of … Read more
Resource leveling is a variant of resource-constrained project scheduling in which a non-regular objective function, the resource availability cost, is to be minimized. We present a branch-and-price approach together with a new heuristic to solve the more general turnaround scheduling problem. Besides precedence and resource constraints, also availability periods and multiple modes per job have … Read more
Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise … Read more
We report on experiments with turning the branch-cut-and-price framework SCIP into a generic branch-cut-and-price solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, … Read more
We propose a Gauss-Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by Andre and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of … Read more