Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

Vsevolod I. Ivanov

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Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

机译：伪凸函数和半严格拟凸函数的刻画

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摘要

In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke-Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to Mangasarian (Oper Res Lett 7:21-26, 1988). A positive function p appears in the most results. It is replaced by the number 1 if the function is convex and its domain of definition is convex, too.

机译：在本文中，我们根据Clarke-Rockafellar次微分，为给定适当的扩展实值函数的拟凸性和半严格拟凸性提供了一些新的充要条件。此外，我们将具有伪凸目标函数的程序扩展到由于Mangasarian而导致的一组约束非线性规划问题的解集的两个较早的刻画（Oper Res Lett 7：21-26，1988）。正函数p出现在大多数结果中。如果函数是凸的并且其定义域也是凸的，则将其替换为数字1。

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来源
《Journal of Global Optimization》 |2013年第3期|677-693|共17页
作者
Vsevolod I. Ivanov;
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作者单位

Department of Mathematics, Technical University of Varna, 1 Studentska Sir, 9010 Varna, Bulgaria;

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正文语种 eng
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关键词
Pseudoconvex functions; Semistrictly quasiconvex functions; Nonsmooth analysis; Characterizations of the solution set of a set constrained optimization problem; Optimality conditions;

机译：伪凸函数;半严格拟凸函数;非平滑分析;集合约束优化问题的解集的刻画;最优条件;

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8. Second Order Characterizations of Pseudoconvex Functions. [R] . Avriel, M., Schaible, S. 1975

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Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

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