We consider a single-period portfolio selection problem which consists of minimizing the total transaction cost subject to different types of constraints on feasible portfolios. The transaction cost function is separable, i.e., it is the sum of the transaction cost associated with each trade, but discontinuous. This optimization problem is nonconvex and very hard to solve. We investigate in thi...

We consider low-rank semidefinite programming (LRSDP) relaxations of unconstrained {−1, 1} quadratic problems (or, equivalently, of Max-Cut problems) that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a ne...

We develop an approximation algorithm for a dynamic capacity allocation problem with Markov modulated customer arrival rates. For each time period and each state of the modulating process, the algorithm approximates the dynamic programming value function using a concave function that is separable across resource inventory levels. We establish via computational experiments that our algorithm inc...

We consider the problem of minimizing a convex linear-fractional separable function over a feasible region defined by a convex inequality constraint or linear inequality constraint, and bounds on the variables (box constraints). These problems are interesting from both theoretical and practical points of view because they arise in somemathematical programming problems and in various practical p...

This special class of a nonlinear mathematical programming problem which is addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method and the notion of superbasics, ha...

the pupose of this paper is modeling of partial digest problem (pdp) as a mathematical programming problem. in this paper we present a new viewpoint of pdp. we formulate the pdp as a continuous optimization problem and develope a method to solve this problem. finally we constract a linear programming model for the problem with an additional constraint. this later model can be solved by the simp...

The aim of this manuscript is to approach by means first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (...

In practice, there are many problems which decision parameters are fuzzy numbers, and some kind of this problems are formulated as either possibilitic programming or multi-objective programming methods. In this paper, we consider a multi-objective programming problem with fuzzy data in constraints and introduce a new approach for solving these problems base on a combination of the multi-objecti...