Ismael Vaz



:: Departamento de Produção e Sistemas ::
:: Escola de Engenharia ::
:: Campus de Gualtar ::
4710-057 Braga - Portugal


:: aivaz at ::

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Sparse and Smoothing Methods for Nonlinear Optimization of Complex Models
Research grant PTDC/MAT/116736/2010 funded by FCT.
January 2011 - December 20



Sustainable electricity power planning
Research grant PTDC/SEN-ENR/099578/2008 funded by FCT.
January 2010 - December 20



Derivative-Free Optimization: Future Challenges and New Applications
Research grant PTDC/MAT/098214/2008 funded by FCT.
January 2010 - December 20



Derivative-Free Optimization and Applications
Research grant POCI/MAT/59442/2004 funded by FCT.
May 2005 - December 2007



A reduction type method for nonlinear semi-infinite programming
Research grant POCI/MAT/58957/2004 funded by FCT.
May 2005 - May 2008



Semi-infinite programming (SIP) problems are characterized by having a finite number of variables to be optimized subject to an infinite number of constraints. SIP problems appear in several engineering areas where constraints must be satisfied for a period of time or in a given region. Examples of application are robot trajectory planning and air pollution control problems, among others.

There are several ways for solving SIP problems. The reduction technique is the one that produces best numerical results. In spite of existing several reduction type algorithms for SIP proposed in the literature, no publicly or commercial software using a reduction algorithm is available.

The reduction type method consists of transforming the SIP problem into a finite one where the infinite number of constraints are replaced by a finite set which corresponds to the local and global optima of the infinite constraints.

The major drawback of the reduction type methods is the need to compute, at each iteration of the algorithm, all the global and as much local optima as possible of the infinite constraints. To address the global optimization problem it is necessary to extend available algorithms to provide a multi-local optimization framework (to compute all the global and local optima). Some of the existent techniques for multi-local are based on stochastic methods, namely the evolutionary strategies with sharing. These techniques proved to be parameter dependent, as they require a priori knowledge of the number of optima and they are not efficient in the general case. Thus, extensions to particle swarm, evolutionary strategies and simulating annealing for multi-local optimization are to be addressed.

In the finite optimization context, the trust region sequential quadratic programming method based on a filter approach that does not require the use of a merit function, has been subject to significant progress. The use of a linesearch strategy instead of the trust region is yet to be studied.

In this context, the project has two innovative goals: the developement of powerful multi-local optimization algorithms to compute all the global and some local optima of the infinite constraints, using particle swarm, evolution strategies and simulated annealing techniques, and the analysis and implementation of a filter SQP method based on a line search strategy for solving the corresponding finite problem.

The final product will consist of a solver that interfaces with the SIPAMPL modeling language, allowing a fast and easy way to solve SIP problems.

The solver will made be publicly available in an internet web page to be developed.



Fletcher, R. and Leyffer, S. (2001), "Nonlinear Programming without a penalty function", Dundee University Numerical Analysis Report, NA 171 (September, 1997), published electronically in Mathematical Programming (September, 2001).

Goberna, M.Á. and Lopez, M.A. (Eds.) (2001), "Semi-Infinite Programming, Recent advances", Nonconvex Optimization and its Applications series, Kluwer Academic Publishers.

Hettich, R. and Kortanek, K.O. (1993), "Semi-infinite programming: Theory, methods, and applications", SIAM Review, 35(3):380-429. 1993.


Polak, E. (1987), "On the mathematical foundations of nondifferentiable optimization in engineering design", SIAM Review 29(1), pp.21-89.

Reemtsen, R. and Rueckmann, J.-J. (Eds.) (1998) "Semi-Infinite Programming", Nonconvex Optimization and its Applications series, Kluwer Academic Publishers.

Monteiro, M.T.T. (2004), "", Vaz, A.I.F., Fernandes, E.M.G.P. and Gomes, M.P.S.F., 2002, "NSIPS V2.1: Nonlinear Semi-Infinite Programming Solver", Technical report ALG/EF/5-2002,

Vaz, A.I.F., Fernandes, E.M.G.P. and Gomes, M.P.S.F., 2004, "SIPAMPL: Semi-infinite programming with AMPL", ACM Transactions on Mathematical Software, 30(1):47-61.



Doctoral Members: Ismael Vaz (PI), Edite Fernandes, Lino Costa, Teresa Monteiro
Graduate students:
Ana Isabel Pereira, António Antunes, Sofia Rogrigues, Cândida Silva





webdesign: Isabel Espírito Santo