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NUMERICAL NONLINEAR GLOBAL OPTIMIZATION

BOGDAN Constantin, NAN Marin Silviu, MAMARA Nicoleta Loredana, GRECEA Danut

Abstract

Linear programming problems are optimization problems where the objective function and constraints are all linear. Mathematica has a collection of algorithms for solving linear optimization problems with real variables, accessed via LinearProgramming, FindMinimum, FindMaximum, NMinimize, NMaximize, Minimize, and Maximize. LinearProgramming gives direct access to linear program- ming algorithms, provides the most flexibility for specifying the methods used, and is the most efficient for large-scale problems. FindMinimum, FindMaximum, NMinimize, NMaximize, Minimize, and Maximize are convenient for solving linear programming problems in equation and inequality form. The Method option specifies the algorithm used to solve the linear programming problem. Possible values are Automatic, "Simplex", "RevisedSimplex", and "InteriorPoint". The default is Automatic, which automatically chooses from the other methods based on the problem size and precision. The Tolerance option specifies the convergence tolerance. Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient-based methods use first derivatives (gradients) or second derivatives (Hessians). Examples are the sequential quadratic programming (SQP) method, the augmented Lagrangian method, and the (nonlinear) interior point method. Direct search methods do not use derivative information.

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DOI resolver: doi.org/10.5593/sgem2017/21/s07.061

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