Approximating separable nonlinear functions via mixed zero-one programs

Approximating separable nonlinear functions via mixed zero-one programs

We discuss two models from the literature that have been developed to formulate piecewise linear approximations of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating th...

Reducing Mixed-Integer to Zero-One Programs

1. The 0-1 knapsack problem with a single continuous variable (KPC) is a natural extension of the binary knapsack problem (KP), where the capacity is not any longer fixed but can be extended which is expressed by a continuous variable. This variable might be unbounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of KPC...

Lagrangian decomposition of block-separable mixed-integer all-quadratic programs

e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...

Approximating the stability region for binary mixed-integer programs

We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution is the polyhedral set of objective coefficients for which the solution is optimal. Knowledge of this set provides valuable information for sensitivity analysis and re-optimization. An exact description of the stability region may requi...

Electronic Companion — “ Mixed Zero - One Linear Programs Under Objective Uncertainty : A Completely Positive Representation ”