OPTIMA swMATH ID: 25286 Software Authors: Bartholomew-Biggs, Michael Description: 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. Homepage: https://link.springer.com/chapter/10.1007/978-0-387-78723-7_25 Keywords: nonlinear programming; unconstrained optimization; constrained optimization Related Software: tn; L-BFGS; WORHP; ALGENCAN; MINOS; Ipopt; TANGO; filterSQP; CUTE; CUTEr; AlphaECP; MINQ; MCS; simannf90 Cited in: 14 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Nonlinear optimization with engineering applications. Zbl 1167.90001Bartholomew-Biggs, Michael 2008 all top 5 Cited by 37 Authors 2 Andrei, Neculai 2 Anndif, M. 2 Nigro, P. S. B. 2 Pimenta, Paulo M. 2 Teixeira, Y. 2 Wriggers, Peter 1 Abdelkhalik, Ossama 1 Abul Bashar, M. 1 Ali, Montaz M. 1 Andreani, Roberto 1 Bai, Yizhou 1 Bartholomew-Biggs, Michael C. 1 Chen, Guanrong 1 Denysiuk, Roman 1 Duan, Peihu 1 Duan, Zhisheng 1 Espirito Santo, Isabel C. P. 1 Fang, Haitao 1 Fernandes, Edite M. G. P. 1 Haeser, Gabriel 1 Hashorva, Enkelejd 1 He, Xingkang 1 Hipel, Keith William 1 Kilgour, D. Marc 1 Liu, Yusong 1 Oliphant, Terry-Leigh 1 Ratovomirija, Gildas 1 Schuverdt, María Laura 1 Secchin, Leonardo D. 1 Shi, Ling 1 Silva, Paulo J. S. 1 Tamraz, Maissa 1 Wang, Jian 1 Wu, Shujun 1 Xue, Wenchao 1 Zhang, Bingjie 1 Zhang, Xiaocheng all top 5 Cited in 12 Serials 2 Automatica 2 Journal of Optimization Theory and Applications 1 Fuzzy Sets and Systems 1 International Journal for Numerical Methods in Engineering 1 Computational Mechanics 1 Neural Networks 1 Journal of Global Optimization 1 Numerical Algorithms 1 Scandinavian Actuarial Journal 1 Mathematical Programming Computation 1 Journal of Mathematical Modelling and Algorithms in Operations Research 1 Springer Optimization and Its Applications all top 5 Cited in 9 Fields 8 Operations research, mathematical programming (90-XX) 6 Numerical analysis (65-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) Citations by Year