OPTIMIZATION WITH LINEAR COMPLEMENTARITY CONSTRAINTS

A Mathematical Program with Linear Complementarity Constraints (MPLCC) is an optimization problem where a continuously differentiable function is minimized on a set defined by linear constraints and complementarity conditions on pairs of complementary variables. This problem finds many applications in several areas of science, engineering and economics and is also an important tool for the solution of some NP-hard structured and nonconvex optimization problems, such as bilevel, bilinear and nonconvex quadratic programs and the eigenvalue complementarity problem. In this paper some of the most relevant applications of the MPLCC and formulations of nonconvex optimization problems as MPLCCs are first presented. Algorithms for computing a feasible solution, a stationary point and a global minimum for the MPLCC are next discussed. The most important nonlinear programming methods, complementarity algorithms, enumerative techniques and 0 - 1 integer programming approaches for the MPLCC are reviewed. Some comments about the computational performance of these algorithms and a few topics for future research are also included in this survey

Cost minimization of a multiple section power cable supplying several remote telecom equipment

Abstract An optimization problem is described, that arises in telecommunications and is associated with multiple cross-sections of a single power cable used to supply remote telecom equipments. The problem consists of minimizing the volume of copper material used in the cables and consequently the total cable cost. Two main formulations for the problem are introduced and some properties of the functions and constraints involved are presented. In particular it is shown that the optimization problems are convex and have a unique optimal solution. A Projected Gradient algorithm is proposed for finding the global minimum of the optimization problem, taking advantage of the particular structure of the second formulation. An analysis of the performance of the algorithm for given real-life problems is also presented

How to make industrial symbiosis profitable

Industrial symbiosis can well represent a new kind of collaborative network which demands resolute attention to the flow management of materials, by-products, and waste through local and regional economies. Industrial symbiosis engages traditionally separate companies in a collaborative approach to competitive advantage involving physical exchange of different kind of products which are usually disregard by traditional market transitions. The identification of innovative models to support decision-making process in this kind of networks is urgent since it is necessary to close the loop assuring profitability at a single node as well as at system level. This paper proposes the application of the bi-level optimization model as a way to handle this two-stage problem organized into two cooperating layers. As a preliminary result, the model is applied to a simplified case where the nodes can sell their output to the market or share them in the industrial symbiosis to increase the global efficiency