Numerical Studies: Comparisons

Abstract

As already seen, for solving nonlinear optimization applications we have a multitude of algorithms and codes integrated in GAMS which involve the theoretical concepts of the augmented Lagrangian, of sequential linear-quadratic or quadratic programming, of generalized reduced gradient, of interior point methods with line-search or interior point methods with trust region or filter, etc. All these algorithms work in conjunction with advanced linear algebra concepts, especially for solving positive definite or indefinite large-scale linear algebraic systems. Always, the performances of optimization algorithms crucially depend on the capabilities of linear algebra algorithms, on linear search, on filter, etc. On the other hand, for solving nonlinear optimization applications from different domains of activity, the present technology involves the usage of algebraic-oriented languages. At present, plenty modeling and optimization technologies are known (Andrei 2013b). The most used, both in academic tests and in real practical applications, are GAMS (Brooke et al. 1998), (Rosenthal 2011), AMPL (Fourer et al. 2002), MPL (Kristjansson 1993), LINDO (Schrage 1997), TOMLAB (Holmstrom 1997), etc.