ABSTRACT

In this paper, we focus on the recession cone and recession function in the nonconvex case. By virtue of the recession function, we investigate the monotonicity of a function. Then, we obtain a characterization of the Lipschitz continuity for a function by using the recession function. As applications, we study the monotonicity and Lipschitz continuity properties of the optimal value function for a parametric constrained optimization problem. Moreover, we present a characterization of the nonemptiness and boundedness of the solution set for a constrained optimization problem without convexity assumption.

中文翻译：

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衰退函数及其在优化中的应用

摘要

在本文中，我们关注非凸情况下的衰退锥和衰退函数。凭借衰退函数，我们研究了函数的单调性。然后，我们通过使用衰退函数获得函数的 Lipschitz 连续性的表征。作为应用，我们研究了参数约束优化问题的最优值函数的单调性和 Lipschitz 连续性特性。此外，我们提出了一个没有凸性假设的约束优化问题的解集的非空性和有界性的特征。