By David Gao, Ning Ruan, Wenxun Xing
This complaints 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 conception; topology optimization; variational inequalities and complementarity difficulties; numerical optimization; stochastic types and simulation and intricate simulation and provide chain research.
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Additional info for Advances in Global Optimization
Heuristic methods for linear multiplicative programming. J. Glob. Optim. 4, 433–447 (1999) 9. : A new linearization method for generalized linear multiplicative programming. Comput. Oper. Res. 38, 1008–1013 (2011) 10. : Global optimization of multiplicative programs. J. Glob. Optim. 26, 387–418 (2003) 11. : A finite branch-and-bound algorithm for linear multiplicative programming. Comput. Optim. Appl. 20, 119–35 (2001) A Modified Cut-Peak Function Method for Global Optimization Sun Li and Wang Yuncheng Abstract We present a cut-peak function method for finding a global minimizer of the bound constrained optimization problems.
When obtaining such a point, let it be the next iteration and return to Phase 1. If such a point does not found, stop the algorithm and return the current iteration xk as the global solution to the original problem. S. Li ( ) • W. cn © Springer International Publishing Switzerland 2015 D. Gao et al. 1007/978-3-319-08377-3__6 51 52 S. Li and W. Yuncheng The cut-peak function method has been initially introduced by Wang . In this method, a cut-peak function and a choice function are defined at a local minimizer, and minimizing the choice function assures a global descent of the original objective function.
X/ on D. x/ on D. e. 7) is equivalent to (SC1) or (SC2) or (SC3) according to the index i . 8) 38 Y. Wang et al. 7)and (SC2–SC3) when i 2 I3 . (1) When i 2 I1 [ I2 [ I4 , we will show that under the following three cases. Case 1. xN i D ui ,. xi 2 1. e. 7) holds. 7) holds, (SC1) is also true. We omit the proof. ] Case 2. xN i D vi . In this case Q i D 1. 7) holds, (SC1) is also true. The proof is also omitted. ] Case 3. ui ; vi /. a C Ax/ N i obviously. 7) holds. a C Ax/ N i D 0. So (SC1) holds.