A Unifying Theory of Exactness of Linear Penalty Functions
M. V. Dolgopolik
备注：
This is a slightly edited version of Accepted Manuscript of an article published by Taylor & Francis in Optimization on 22/12/2015, available online: http://www.tandfonline.com/10.1080/02331934.2015.1122005. In this version, a remark was added after Proposition 3.6 (the original numbering was preserved), and a mistake in the proof of Theorem 3.17 was corrected
In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally exact linear penalty functions, and obtain various necessary and sufficient conditions for the exactness of a linear penalty function. We pay more attention than usual to necessary conditions that allows us to deeper understand the exact penalty technique.
A unifying theory of exactness of linear penalty functions II: parametric penalty functions
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems . The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions , and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parame…
Exact Penalty Algorithm of Strong Convertible Nonconvex Optimization
This paper defines a strong convertible nonconvex(SCN) function for solving the unconstrained optimization problems with the nonconvex or nonsmooth(nondifferentiable) function. First, many examples of SCN function are given, where the SCN functions are nonconvex or nonsmooth. Second, the operational properties of the SCN functions are proved, including addition, multiplication, compound operations and so on. Third, the SCN forms of some special functions common in machine learning and engineering applications are presented respectively where these SCN function optimization problems can be tran…
Fast and Effective Computation of Generalized Symmetric Matrix Factorization
School of Computer Science and Engineering（计算机科学与工程学院）；Guangdong Province Key Laboratory of Computational Science（广东省计算科学重点实验室）；Sun Yat-sen University（中山大学）；School of Mathematics and Information Science（数学与信息科学学院）；Guangzhou University（广州大学）；Department of Mathematics（数学系）；The University of Tennessee, Knoxville（田纳西大学，诺克斯维尔）
