Recession function and its applications in optimization. (2nd December 2021)

• Record Type: Journal Article
• Authors: Li, Genghua; Li, Shengjie; You, Manxue
• Is Part Of: Optimization. Volume 70:Number 12(2021)
• Page Start: 2559
• Page End: 2578
• Publication Date: 2021-12-02
• Subjects: Recession cone -- asymptotic cone -- recession function -- monotonicity -- Lipschitz continuity; 90C26 -- 90C30 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1786569
• Languages: English
• ISSNs: 0233-1934

Abstract

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.