OPTIMA

Nonlinear optimization with engineering applications. This book gives on 280 pages a broad overview of nonlinear optimization. The presented methods include direct search techniques, the steepest descend approach, trust region methods as well as Newton and quasi-Newton techniques with globalization strategies for the unconstrained case. For constrained optimization problems penalty approaches, SQP methods, barrier techniques and interior point methods are discussed. Additionally, the book covers several topics as line search approaches, filter methods and the computation of derivatives. The presented optimization approaches are compared with each other by means of several examples with up to 200 variables. The numerical results are mostly obtained by the software package OPTIMA written by the author. The book contains 25 chapters with an average of 11 pages. Due to the variety of considered solution techniques, the presentation of each method and its theoretical analysis is rather brief. Nevertheless, the introduction of the different techniques is written in a very comprehensible way. Furthermore, each section contains exercises to verify and deepen the understanding of the material.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Andrei, Neculai: Diagonal approximation of the Hessian by finite differences for unconstrained optimization (2020)
  2. Duan, Peihu; Duan, Zhisheng; Chen, Guanrong; Shi, Ling: Distributed state estimation for uncertain linear systems: a regularized least-squares approach (2020)
  3. He, Xingkang; Xue, Wenchao; Zhang, Xiaocheng; Fang, Haitao: Distributed filtering for uncertain systems under switching sensor networks and quantized communications (2020)
  4. Andrei, Neculai: A diagonal quasi-Newton updating method for unconstrained optimization (2019)
  5. Zhang, Bingjie; Liu, Yusong; Cao, Jinde; Wu, Shujun; Wang, Jian: Fully complex conjugate gradient-based neural networks using Wirtinger calculus framework: deterministic convergence and its application (2019)
  6. Hashorva, Enkelejd; Ratovomirija, Gildas; Tamraz, Maissa; Bai, Yizhou: Some mathematical aspects of price optimisation (2018)
  7. Oliphant, Terry-Leigh; Ali, M. Montaz: A trajectory-based method for mixed integer nonlinear programming problems (2018)
  8. Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P.: An adaptive model order reduction with quasi-Newton method for nonlinear dynamical problems (2016)
  9. Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P.: An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems (2016)
  10. Espirito Santo, Isabel C. P.; Denysiuk, Roman; Fernandes, Edite M. G. P.: Derivative-free augmented Lagrangian for global optimization: cost minimization in a simplified activated sludge system model (2015)
  11. Bashar, M. Abul; Kilgour, D. Marc; Hipel, Keith W.: Fuzzy option prioritization for the graph model for conflict resolution (2014)
  12. Abdelkhalik, Ossama: Hidden genes genetic optimization for variable-size design space problems (2013)
  13. Bartholomew-Biggs, Michael: Nonlinear optimization with engineering applications (2008)