In optimal short-term resource scheduling decomposition and coordination methods by Lagrangean relaxation are known as convenient to handle resource-specific constraints and for their ability to provide duality gap estimates. They will be used, in context of subgradient optimization, to deal with this problem. One cause of erratic behavior often encountered in subgradient optimization is associ...

We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the first survey that connects the two very important areas. We further look at a similar phenomenon in finite model theory relating to complexity and optimization.

We consider multistage stochastic optimization models containing nonconvex constraints, e.g., due to logical or integrality requirements. We study three variants of Lagrangian relaxations and of the corresponding decomposition schemes, namely, scenario, nodal and geographical decomposition. Based on convex equivalents for the Lagrangian duals, we compare the duality gaps for these decomposition...

This paper reports the results of a study into the effectiveness of the SPARK toolset for showing the absence of run-time errors in safety-critical Ada software. In particular, the toolset is examined to determine how effective it is in finding run-time errors in a SPARK program, and how much of the process of proving freedom from run-time errors can be performed automatically. The study identi...

Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the socalled safe rules for the Lasso. Based on duality gap considerations, our new rules create safe test regions whose diameters converge to zero, provided that one relies on a converging solver. This property...

We present a procedure for constructing a group theoretic dual problem with no duality gap to a given bounded integer programming problem. An optimal solution of this dual problem is easily determined and an optimal solution of the integer programming problem can be obtained by solving only one group optimization problem.

Anticipatory algorithms for online stochastic optimization have been shown very effective in a variety of areas, including logistics, reservation systems, and scheduling. For such applications which typically feature purely exogenous uncertainty, the one-step anticipatory algorithm was shown theoretically to be close to optimal when the stochasticity of the problem, measured by the anticipatory...

We demonstrate how the pricing problem for electricity swing options can be considered as a stochastic bilevel program with asymmetric information. Unlike as for nancial options, there is no way for basing the pricing method on no-arbitrage arguments. Two main situations are analyzed: If the seller has strong market power he/she might be able to maximize his/her utility, while in fully competit...

We consider the Bayesian ranking and selection problem, with independent normal prior, independent samples, and a sampling cost. While several procedures have been developed for this problem in the literature, the gap between the best existing procedure and the Bayes-optimal one remains unknown, because computing the Bayes-optimal procedure using existing methods requires solving a stochastic d...