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...

We discuss recent advances in mathematical programs with equilibrium constraints (MPECs). We describe the challenges posed by these problems and the current algorithmic solutions. We emphasize in particular the use of the elastic mode approach. We also present initial investigations in applications of MPECs to control problems.

The pruning power of partial symmetry breaking depends on the given subset of symmetries to break as well as the interactions among symmetry breaking constraints. In the context of Partial Symmetry Breaking During Search (ParSBDS), the search order determines the set of symmetry breaking constraints to add and thus also makes an impact on node and solution pruning. In this paper, we give the fi...

Conditional symmetry arises in a sub-problem of a constraint satisfaction problem, where the sub-problem satisfies some condition under which additional symetries hold. Typically, the condition is a set of assignments of values to variables, i.e. a partial assignment reached during systematic search. Like unconditional symmetry, conditional symmetry can cause redundancy in a systematic search f...

We study an oligopoly consisting of M leaders and N followers that supply a homogeneous product (or service) noncooperatively. Leaders choose their supply levels first, knowing the demand function only in distribution. Followers make their decisions after observing the leader supply levels and the realized demand function. We term the resulting equilibrium a stochastic multiple-leader Stackelbe...

This paper studies stability for parametric mathematical programs with geometric constraints. We show that, under the no nonzero abnormal multiplier constraint qualification and the second-order growth condition or second-order sufficient condition, the locally optimal solution mapping and stationary point mapping are nonempty-valued and continuous with respect to the perturbation parameter and...

The problem of finding a next best viewpoint for 3D modeling or scene mapping has been explored in computer vision over the last decade. This paper tackles a similar problem, but with different characteristics. It proposes a method for dynamic next best viewpoint recovery of a target point while avoiding possible occlusions. Since the environment can change, the method has to iteratively find t...

In this paper the workspace optimization of translational 3-UPU parallel platforms with prismatic and universal joint constraints is performed. The workspace is parameterized using two design parameters, which are the prismatic joint stroke and the difference between the distances of the center to one of the corners of the triangular plate of the base and of the moving platform. For a large ran...

We study Nash equilibrium in two-settlement competitive electricity markets with horizontal market power, flow congestion, demand uncertainties and probabilistic system contingencies. The equilibrium is formulated as a stochastic Equilibrium Problem with Equilibrium Constraints (EPEC) in which each firm solves a stochastic Mathematical Program with Equilibrium Constraints (MPEC). We assume a no...

We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle tech...