A Loss Function for Box-Constrained Inverses Problems

Box-Constrained Approach for Hard Permutation Problems

Algorithm 3 details the process for incrementally computing term (13) for all xk. (The process for computing (14) is similar.) Computation of the full gradient is thus also an O(nm) operation. Using this technique, we can apply full-gradient first-order methods efficiently, including gradient projection and Frank-Wolfe. With an appropriate line-search method, gradient projection is guaranteed t...

A Hybrid Newton Method for Solving Box Constrained Variational Inequality Problems via the D-gap Function

A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.

A Box-Constrained Approach for Hard Permutation Problems

We describe the use of sorting networks to form relaxations of problems involving permutations of n objects. This approach is an alternative to relaxations based on the Birkhoff polytope (the set of n × n doubly stochastic matrices), providing a more compact formulation in which the only constraints are box constraints. Using this approach, we form a variant of the relaxation of the quadratic a...

A box-constrained differentiable penalty method for nonlinear complementarity problems

Uniqueness of Generalized Equilibrium for Box Constrained Problems and Applications

In recent work, Simsek-Ozdaglar-Acemoglu [5] prove a generalization of the Poincare-Hopf Theorem and establish sufficient conditions for the uniqueness of generalized critical points (generalized equilibria) under some regularity assumptions. In this paper, we restrict ourselves to functions on box-constrained regions and establish the uniqueness of the generalized critical point with weaker re...