L.A. Wolsey * A class of strong valid inequalities is described for the single-item uncapacitated economic lot-sizing problem with start-up costs. It is shown that these inequalities yield a complete polyhedral characterization of the problem. The corresponding separation problem is formulated as a shortest path problem. Finally, a reformulation as a plant location problem is shown to imply the...

Inspired by the optimal value approach, we propose a new reformulation of the optimistic Bilevel programming Problem (BP) as a suitable Generalized Nash Equilibrium Problem (GNEP). We provide a complete analysis of the relationship between the original hierarchical BP and the corresponding “more democratic” GNEP. Moreover, we investigate solvability and convexity issues of our reformulation. Fi...

We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by adding new variables and reformulating into non-convex program with linear constraints (MIQP). then consider solution of (MIQP) specially-tailored reformulation method. In particula...

Automatic design optimization is highly sensitive to problem formulation. The choice of objective function, constraints and design parameters can dramatically impact the computational cost of optimization and the quality of the resulting design. The best formulation varies from one application to another. A design engineer will usually not know the best formulation in advance. We have therefore...

A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of scalar fields for classical position/momentum observables Q/P , QM evolves (in Heisenberg’s picture) according to the formally similar Lie algebra of commutator ...

According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient...

The intelligent reformulation or restructuring of a be­ lief network can greatly increase the efficiency of in­ ference. However, time expended for reformulation is not available for performing inference. Thus, un­ der time pressure, there is a tradeoff between the time dedicated to reformulating the network and the time applied to the implementation of a solution. We investigate this partition...

This problem will be studied at an heuristic level, i.e., in a way similar to the theory of the critical point in d = 4 ? " dimensions (see chapters 9 and 10). One should not forget that the latter problem, considered by many one of the major successes of the renormalization group approach, is still awaiting a rigorous formulation, not only for " = 1, but also for any " > 0. Therefore, we think...

A New Family of Valid-Inequalities for Dantzig-Wolfe Reformulation Mixed Integer Linear Programs In “Consistency Cuts Reformulation,” Jens Vinther Clausen, Richard Lusby, and Stefan Ropke present a new family valid inequalities to be applied reformulations with binary linking variables. They show that, mixed integer linear programs that satisfy certain properties, it is enough solve the program...