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Download PDF by Brand L.: Advanced Calculus

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Furthermore, the tools used to derive optimality conditions are also different. 2 Preliminaries Our goal is to formulate the bilevel programming problem as a multiobjective programming problem. In a multiobjective problem, we are interested in optimizing an objective mapping with a multi-dimensional range space. An order in the range space is defined through a set and the objective is to find a point zN such that no other points in the constraint set of the domain space give better objective values.

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.

Since the pattern search method does not require the gradient of the choice function, smoothing technique is not employed. The new algorithm is simple to implement and numerical results indicate its efficiency. 1 Introduction The global optimization algorithms play an important role in real-world applications, but the definition of an efficient algorithm for these problems is an open question. In literature, many different approaches have been proposed to solve this class of problems. One of these is the function modification approach, such as the filled function methods [1–4], the tunneling methods [5], and the cut-peak function methods [6,7].

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Advanced Calculus by Brand L.

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