We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (2010) and uses Benders decomposition to form a master problem and a subproblem. The new...

Symmetry Breaking During Search (SBDS) adds conditional symmetry breaking constraints (which are nogoods) dynamically upon backtracking to avoid exploring symmetrically equivalents of visited search space. The constraint store is proliferated with numerous such individual nogoods which are weak in constraint propagation. We introduce the notion of increasing nogoods, and give a global constrain...

Despite evidence that consumers search across both stores (spatial) and time (temporal), the search literature models search in only one dimension. We develop a model of spatiotemporal search that nests a finite horizon model of spatial search within an infinite horizon model of intertemporal search. The model is estimated using an iterative procedure that formulates it as a mathematical progra...

We have analysed 53 square degrees of RC -band imaging data from the Red-Sequence Cluster Survey (RCS), and measured the excess correlations in the shapes of galaxies on scales out to ∼ 1.5 degrees. We separate the signal into an “E”(lensing) and “B”-mode (systematics), which allows us to study residual systematics. On scales larger than 10 arcminutes, we find no “B”-mode, suggesting that the s...

In this paper, we consider the stochastic mathematical program with equilibrium constraints (SMPEC), which can be thought as a generalization of the mathematical program with equilibrium constraints. Many decision problems can be formulated as SMPECs in practice. We discuss both here-and-now and lower-level wait-and-see decision problems. In particular, with the help of a penalty technique, we ...

In this paper, an algorithm for solving a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be ...

The paper presents a simulation of the deployment/retraction of a solid surface deployable reflector recently developed at Cambridge University. The simulation takes proper account of the contacts that can develop between panels of adjacent wings of the reflector, by implementing the theory for tracing the equilibrium path of a mechanical system with unilateral constraints that has been propose...

If a mathematical program has many symmetric optima, solving it via Branchand-Bound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for automatically finding the formulation group of any given Mixed-Integer Nonlinear Program, and for reformulating the problem by means of static symmetry breaking co...

1 We extend the existing toll pricing studies with fixed demand to stochastic demand. A new and 2 practical second-best pricing problem with uncertain demand is proposed and formulated as a 3 stochastic mathematical program with equilibrium constraints. In view of the problem structure, 4 we develop a tailored global optimization algorithm. This algorithm incorporates a sample 5 average approxi...

The past few years have seen significant progress in algorithms and heuristics for both SAT and symmetry detection. Additionally, the thesis that some of SAT’s intractability can be explained by the presence of symmetry, and that it can be addressed by the introduction of symmetry-breaking constraints, was tested, albeit only to a rather limited extent. In this paper we explore further connecti...