We present a hierarchy of semidefinite programming (SDP) relaxations for solving the concave cost transportation problem (CCTP), which is known to be NP-hard, with $p$ suppliers and $q$ demanders. In particular, we study cases in which the cost function is quadratic or square-root concave. The key idea of our relaxation methods is in the change … Read more
A well-known approach to the design of computationally efficient filters is to use spectral factorization, i.e. a decomposition of a filter into a sequence of sub-filters. Due to the sparsity of the sub-filters, the typical processing speedup factor is within the range 1-10 in 2D, and for 3D it achieves 10-100. The design of such … Read more
We present an algorithm for the minimization of f : Rn → R, assumed to be locally Lipschitz and continuously differentiable in an open dense subset D of Rn. The objective f may be non-smooth and/or non-convex. The method is based on the gradient sampling (GS) algorithm of Burke et al. [A robust gradient sampling … Read more
This paper provides a new multi-objective integer programming model for the daily scheduling of nurses in operating suites. The model is designed to assign nurses to di erent surgery cases based on their specialties and competency levels, subject to a series of hard and soft constraints related to nurse satisfaction, idle time, overtime, and job changes … Read more
The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. In this article, we propose an outer approximation algorithm for maximizing a function $h(x) = \varphi(f(x))$ over the efficient set $X_E$ of the bi-criteria convex programming problem $ {\rm Vmin} \{f(x)=(f_1(x), f_2(x))^T … Read more
We consider the problem of minimizing a continuously di erentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the rst order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class … Read more
This paper is a continuation of the paper Kakihara, Ohara and Tsuchiya by the authors where they demonstrated that the number of iterations of Mizuno-Todd-Ye predictor-corrector primal-dual interior-point methods for SDP and more generally symmetric cone programs is (asymptotically) expressed with an integral over the central trajectory called “curvature integral.” It was shown that the … Read more
This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the … Read more
We propose an algorithm that computes the epsilon-correlated equilibria with global-optimal (i.e., maximum) expected social welfare for single stage polynomial games. We first derive an infinite-dimensional formulation of epsilon-correlated equilibria using Kantorovich polynomials and re-express it as a polynomial positivity constraint. In addition, we exploit polynomial sparsity to achieve a leaner problem formulation involving Sum-Of-Squares … Read more
Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out … Read more