Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes

Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes

Multiplicative programming problems (MPPs) are global optimisation problems known to be NP-hard. In this paper, we employ algorithms developed to compute the entire set of nondominated points of multi-objective linear programming (MOLP) problems to solve linear MPPs. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solv...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

Long-step primal-dual target-following algorithms for linear programming

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract In this paper we propose a method for linear programming with the property that, starting from an initial non{central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow so{called targets, that are updated with long steps. Newto...

Primal-Dual Projected Gradient Algorithms for Extended Linear-Quadratic Programming

Many large-scale problems in dynamic and stochastic optimization can be modeled with extended linear-quadratic programming, which admits penalty terms and treats them through duality. In general the objective functions in such problems are only piecewise smooth and must be minimized or maximized relative to polyhedral sets of high dimensionality. This paper proposes a new class of numerical met...

Primal-Dual Enumeration for Multiparametric Linear Programming

Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (pLPs) and solved explicitly offline. Several algorithms have recently been proposed in the literature that solve these pLPs in a fairly efficient manner, all of which have as a base operation the computation and removal of redundant constraints. For many problems, it is th...