By David Gao, Ning Ruan, Wenxun Xing

This court cases quantity addresses advances in international optimization—a multidisciplinary study box that bargains with the research, characterization and computation of worldwide minima and/or maxima of nonlinear, non-convex and nonsmooth services in non-stop or discrete varieties. the amount comprises chosen papers from the 3rd biannual international Congress on international Optimization in Engineering & technology (WCGO), held within the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into 8 topical sections: mathematical programming; combinatorial optimization; duality idea; topology optimization; variational inequalities and complementarity difficulties; numerical optimization; stochastic types and simulation and complicated simulation and provide chain analysis.

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Variational Analysis. Grundlehren der Mathematischen Wissenschafte, vol. 317. Springer, Berlin (1998) 8. : Methods of variational analysis in multiobjective optimization. Optimization 58(4), 413–430 (2009) 9. : On calculating the normal cone to a finite union of convex polyhedra. Optimization 57, 57–78 (2008) Global Sufficient Conditions for Nonconvex Cubic Minimization Problem with Box Constraints Yanjun Wang, Zhian Liang, and Linsong Shen Abstract In this paper, we focus on deriving some sufficient conditions for global solutions to cubic minimization problems with box constraints.

Moreover, research results about Y. Wang ( ) • Z. Liang • L. cn © Springer International Publishing Switzerland 2015 D. Gao et al. 1007/978-3-319-08377-3__4 33 34 Y. Wang et al. cubic optimization problem can be applied to quadratic programming problems, which have been widely studied because of its broad applications, to enrich quadratic programming theory. Several general approaches can be used to establish optimality conditions for solutions to optimization problems [4–8]. These approaches can be broadly classified into three groups: convex duality theory, local subdifferentials by linear functions, global L-subdifferential and L-normal cone by quadratic functions.

R is an overestimator of the function f W Rn ! x/. N The function h W Rn ! R is an underestimator of the function f W Rn ! x/. 5. xN 1 ; ; xN n / 2 R . Suppose that there exists a diagonal matrix Q such that P A Q 0. A Q/xN C a/T x. x/ N is a cubic underestimator over Rn . Proof. 4. x/ at xN over D. 3 Sufficient Conditions for the Solution to Cubic Programming with Box Constraints We define four index sets I1 ; ; I4 according to the given point xN at first and make sure that [4iD1 Ii D f1; 2; ; ng.