Strekalovsky, Alexander S. On solving optimization problems with hidden nonconvex structures. (English) Zbl 1335.90075 Rassias, Themistocles M. (ed.) et al., Optimization in science and engineering. In honor of the 60th birthday of Panos M. Pardalos. New York, NY: Springer (ISBN 978-1-4939-0807-3/hbk; 978-1-4939-0808-0/ebook). 465-502 (2014). The author considers the following, in general, non-convex problems: linear complementarity problems with indefinite matrices, the Nash equilibrium in bi-matrix games and the “optimistic” solution in quadratic-linear bi-level optimization problems. The “optimistic” solution means that the upper level (leader) and lower level (follower) are searching a common solution in cooperation. Properties of these problems are studied and a new approach to solving the problems is presented. The new approach is based on global optimality conditions, local search methodology and global search methodology. Computational experience with the new procedures and its comparison with other methods (especially with software KNITRO) show that the procedures proposed in the paper are proved to be competitive.For the entire collection see [Zbl 1291.90008]. Reviewer: Karel Zimmermann (Praha) Cited in 1 ReviewCited in 20 Documents MSC: 90C26 Nonconvex programming, global optimization 90C30 Nonlinear programming 90C20 Quadratic programming Keywords:non-convex optimization; global optimality condition; local search methodology; global search methodology PDFBibTeX XMLCite \textit{A. S. Strekalovsky}, in: Optimization in science and engineering. In honor of the 60th birthday of Panos M. Pardalos. New York, NY: Springer. 465--502 (2014; Zbl 1335.90075) Full Text: DOI