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.

In this paper a truss-structure model is described for finding a kinematically stable structure with optimal topology and cross-sectional size and minimum volume. The underlying model findsapplicationsinsomecivil engineering structuraldesignproblemsand takes into consideration all the conditions associated with the limit states usually presented in structural safety codes. Ultimate limit states are treated applying plasticity theory, while serviceability limit states are dealt with via elasticity theory. The admissible solution space is discretised using bar elements. A 0 − 1 variable is assigned to each one of these elements, in order to indicate if it is or not included in the solution. The mathematical formulation of the model leads to a mixed 0 1 integer nonlinear program with a nonlinear objective function and linear and bilinear constraints. It is shown that this problem can be reduced into a mixed 0 1 integer linear program by exploiting the so- called reformulation-linearization technique. Some computational experience is included to highlight the importance of these formulations in practice.

Neste artigo é discutido um modelo desenvolvido por Konno para a selecção de carteiras de activos financeiros e o seu desempenho é comparado com o do modelo clássico de Markowitz. Para além de analisar a velocidade de obtenção de respostas, procura-se avaliar qualitativamente as soluções obtidas e discute-se a efectiva aplicação dos modelos dentro das práticas comuns ao mercado de capitais.

In this paper Konno portfolio selection model is presented and compared with Markowitz classical model. The computational effort for finding an optimal portfolio by both models is investigated and the quality of the corresponding portfolios is analyzed. The use of these two models in real-life capital markets is finally discussed.