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On the solution of the symmetric eigenvalue complementarity problem by the spec...
Júdice, Joaquim; Raydan, Marcos; Rosa, Silvério; Santos, SandraAbstract This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenva...
Cost minimization of a multiple section power cable supplying several remote te...
Júdice, Joaquim; Anunciada, Victor; Baptista, CarlosAbstract 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 c...
The eigenvalue complementarity problem
Júdice, Joaquim; Sherali, Hanif; Ribeiro, Isabel M.Abstract In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique (Rlt)-based tree search algorith...
A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathemat...
Júdice, Joaquim; Sherali, Hanif; Ribeiro, Isabel; Faustino, AnaAbstract 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...
Workforce planning in a lotsizing mail processing problem
Júdice, Joaquim; Martins, Pedro; Nunes, JacintoThe treatment of mail objects in a mail processing centre involves many operations, in particular sorting by destination. Out of the batching problem that we can identify in such a process, there are also staff planning concerns. In this paper, we analyse a treatment area (registered mail) belonging to a mail processing center, where mail objects are treated in a chain production process. The production quantit...
A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorit...
Figueiredo, Isabel N.; Júdice, Joaquim J.; Rosa, Silvério S.We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A ...
A Study of Preconditioners for Network Interior Point Methods
Júdice, Joaquim; Patricio, João; Portugal, Luis; Resende, Mauricio; Veiga, GeraldoWe study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners are tested using PDNET, a state-of-the-art interior point code for the minimum cost network flow problem. A computational comparison using...
On the solution of NP-hard linear complementarity problems
Júdice, Joaquim; Faustino, Ana; Ribeiro, IsabelAbstract 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. ; http://dx.doi....
On the solution of a finite element approximation of a linear obstacle plate pr...
Fernandes, Luís M.; Figueiredo, Isabel N.; Júdice, Joaquim J.In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate tha...
Complementarity and genetic algorithms for an optimization shell problem
Figueiredo, Isabel N.; Júdice, Joaquim J.; Oliveira, Pedro N.The application of complementarity and genetic algorithms to an optimization thin laminated shallow shell problem is discussed. The discrete form of the problem leads to a Mathematical Program with Equilibrium Constraints (MPEC) [1], whose constraint set consists of a variational inequality and a set of equality constraints. Furthermore the variables are discrete. Special instances of the general problem are co...
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