Many reasoning and optimization problems exhibit symmetries. Previous work has shown how special purpose algorithms can make use of these symmetries to simplify reasoning. We present a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory. Our approach can be used on any propo-sitional satissability problem, and can be used as a pre-processor to ...

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the normal-cone mapping related to C2 inequality constraints under very weak qualification conditions. This enables us to provide the graphical derivative and the regular coderivative of the solution map to a class of parameterized generalized equations with the constraint set of the investi...

Symmetry-breaking constraints in the form of inequalities between variables have been proposed for a few kind of solution symmetries in numeric CSPs. We show that, for the variable symmetries among those, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs. We discuss the merits of this relaxation and present exp...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...

Probabilistic design, such as reliability-based design and robust design, offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. Since a probabilistic optimization often involves a double-loop procedure for the overall optimization and iterative probabilistic assessment, the computational demand is extr...

We formulate a two-settlement equilibrium in competitive electricity markets as a subgame-perfect Nash equilibrium in which each generation firm solves a Mathematical Program with Equilibrium Constraints (MPEC), given other firms’ forward and spot strategies. We implement two computational approaches, one of which is based on a Penalty Interior Point Algorithm and the other is based on a steepe...

In this note, we present the necessary mathematical framework for stochastic MPEC models, including some new results on the existence of solutions and on convexity and diierentiability of the implicit upper-level objective function. In so doing, we clarify the links between these models and two-stage stochastic programs with recourse.

We introduce a hierarchical approach for the analysis and design of systems with multiple frictional contacts, with a focus on applications to the design of part feeding and assembly processes. The simplest model in the hierarchy is the geometric model described by a set of non-penetration constraints that depends only on the geometry of the design. The model with the highest fidelity is one th...

Harrington et al. [21] introduced a general framework for modeling tacit collusion in which producing firms collectively maximize the Nash bargaining objective function, subject to incentive compatibility constraints. This work extends that collusion model to the setting of a competitive pool-based electricity market operated by an independent system operator. The extension has two features. Fi...

Symmetries are inherent in systems that consist of several interchangeable objects or components. When reasoning about such systems, big computational savings can be obtained if the presence of symmetries is recognized. In earlier work, symmetries in constraint satisfaction problems have been handled by introducing symmetry-breaking constraints. In reasoning about transition systems, notably in...