Computation of maximal turning points to nonlinear equations by nonsmooth optimization. (2nd January 2016)

• Record Type: Journal Article
• Authors: Il'yasov, Yavdat; Ivanov, Aleksandr
• Is Part Of: Optimization methods and software. Volume 31:Number 1(2016)
• Page Start: 1
• Page End: 23
• Publication Date: 2016-01-02
• Subjects: turning point -- steepest ascent direction -- nonlinear system -- nonsmooth optimization -- quadratic programming problem; 37M20 -- 49K35 -- 65K10 -- 65P30 -- 90C47; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2015.1009978
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We develop a new approach to finding bifurcations of solutions of nonlinear equation systems, which is based on the detection of extreme values of a new type of variational functional associated with the considered problems. The variational functional is obtained constructively by the extended functional method which can be applied to a wide class of parametric problems including nonlinear partial differential equations. Sufficient and necessary conditions for the existence of a maximal turning point by the approach are proved. Based on these, an algorithm of the quasi-direction of steepest ascent is introduced. Simulation experiments are used to illustrate the behaviour of the method and to discuss its advantages and disadvantages in comparison with the alternatives.