Computational Methods of Optimization

Methods for the minimization of functions of a real variable. Methods for unconstrained multidimensional minimizing. Classical methods: gradient methods, Newton method. Quasi-Newton methods, variable metric methods, conjugated direction methods, secante methods. Global convergence of quasi-Newton methods: confidence regions. Multidimensional minimization methods with linear restrictions: dual methods, increased Lagrangean method, reduced gradient method. Multidimensional minimization methods with general restrictions: projected gradient method, internal punishment methods, external punishment methods.

References:
BERTSEKAS, D.P. – Nonlinear Programming. Athena Scientific, 1995.
BONNANS, J.F., GILBERT J-CH., LEMARÉCHAL, C., SAGASTIZÁBAL, C. – Numerical optimization : theoretical and practical aspects. 2nd ed, Berlin; New York. Springer, 2006.
DENNIS JR, J. E., SCHNABEL, R. B. – Numerical methods for unconstrained optimization and nonlinear equations. Corrected reprint of the 1983 original. Classics in Applied Mathematics, 16. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996.
IZMAILOV, A. E., SOLODOV, M. – Otimização, volume 2. Rio de Janeiro, IMPA, 2007.

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