Ana M. Faustino

A sequential LCP method for bilevel linear programming

In this paper, we discuss an SLCP algorithm for the solution of Bilevel Linear Programs (BLP) which consists of solving a sequence of Linear Complementarity Problems (LCP) by using a hybrid enumerative method. This latter algorithm incorporates a number of procedures that reduce substantially the search for a solution of the LCP or for showing that the LCP has no solution. Computational experience with the SLCP algorithm shows that it performs quite well for the solution of small- and medium-scale BLPs with sparse structure. Furthermore, the algorithm is shown to be more efficient than a branch-and-bound method for solving the same problems.

A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

On the Solution of NP-hard Linear Complementarity Problems

In this paper two enumerative algorithms for the Linear Complementarity Problems (LCP) are discussed. These procedures exploit the equivalence of theLCP into a nonconvex quadratic and a bilinear programs. It is shown that these algorithms are efficient for processing NP-hardLCPs associated with reformulations of the Knapsack problem and should be recommended to solve difficultLCPs.

A computational analysis of LCP methods for bilinear and concave quadratic programming

Abstract The use of a sequential linear complementarity problem (SLCP) algorithm for finding a global minimum of bilinear programming problem (BLP) or a concave quadratic program (CQP) is examined. The algorithm consists of solving a sequence of linear complementarity problems (LCP). A branch-and-bound method is also considered in this study. This algorithm is based on the reformulation of a BLP into an LCP with a linear function to minimize. Computational experience with small and medium scale BLPs and CQPs indicates that the SLCP algorithm is quite efficient in finding a global minimum (or at least a solution that is quite near the optimum), but it is, in general, unable to establish that such a solution has been found. An algorithm to find a lower-bound for the BLP can overcome this drawback in some cases. Furthermore the SLCP algorithm is shown to be robust and compares favorably with the branch-and-bound method and another alternative technique.

An experimental investigation of enumerative methods for the linear complementarity problem

Abstract The Linear Complementarity Problem (LCP) is that of finding vectors z ϵ Rn and w ϵ Rn such that w = q + Mz, z ⩾ 0, w ⩾ 0, zTw = 0, where qϵ Rn and M is a n by n real matrix. This problem can be processed by enumerative tree-search methods, whose efficiency depends on a set of strategies to reduce the search. In this paper a number of such strategies is discussed and an experimental investigation of the resulting enumerative methods on small and medium scale (n ⩽ 500) sparse LCPs is presented. The applicability of these methods for general LCPs (without any assumption on the class of the matrix) and the numerical results presented in this paper show that it is worthwhile to use these methods for general medium scale sparse LCPs.

A place for arguing in engineering education: a study on students’ assessments

This paper focuses on the issue of how engineering programmes demand and/or promote argumentative reasoning, which is a subsequent aspect of curricular development. This was the main objective of the project on which this paper reports. This is to say that the focus is on assessment as a way to establish to what extent argumentative reasoning is demanded and mobilised in teaching and learning processes. This aim was achieved using a sample of assignments developed in courses in different Bologna undergraduate programmes at the Engineering School at the University of Porto, during the first semester of the academic year 2009/2010. Whereas problem solving in engineering constitutes a structural element in the curricular organisation of the engineering programmes and is strongly related to argumentative skills, it was possible to conclude that students demonstrate and explain extensively, but do not argue, possibly because their teachers do not invite them to do so in assessment situations.

On the use of bilevel programming for solving a structural optimization problem with discrete variables

In this paper, a bilevel formulation of a structural optimization problem with discrete variables is investigated. The bilevel programming problem is transformed into a Mathematical Program with Equilibrium (or Complementarity) Constraints (MPEC) by exploiting the Karush-Kuhn-Tucker conditions of the follower’s problem.