NDLI: A homotopy method based on penalty function for nonlinear semidefinite programming

Content Provider	Springer Nature Link
Author	Yang, Li Yu, Bo Li, YanXi
Copyright Year	2015
Abstract	This paper proposes a homotopy method based on a penalty function for solving nonlinear semidefinite programming problems. The penalty function is the composite function of an exponential penalty function, the eigenvalue function and a nonlinear operator mapping. Representations of its first and second order derivatives are given. Using the penalty function, a new homotopy is constructed. Global convergence of a smooth curve determined by the homotopy is proven under mild conditions. In the process of numerically tracing the curve, the method requires just the solution of a linear system of dimension $$n+2$$ , whereas a homotopy method proposed by Yang and Yu (Comput Optim Appl 56(1):81–96, 2013) requires a system of dimension $$n+m(m+1)/2+1$$ to be solved, where $$n$$ is the number of variables while $$m$$ is the order of constraint matrix. So, it is expected that the proposed method can improve the efficiency of the method proposed by Yang and Yu. Preliminary numerical experiments are presented and show that the considered algorithm is efficient for some nonlinear semidefinite programming problems.
Starting Page	61
Ending Page	76
Page Count	16
File Format	PDF
ISSN	09255001
Journal	Journal of Global Optimization
Volume Number	63
Issue Number	1
e-ISSN	15732916
Language	English
Publisher	Springer US
Publisher Date	2015-02-08
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Homotopy method Global convergence Penalty function Nonlinear semidefinite programming Optimization Operations Research/Decision Theory Real Functions Computer Science
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A new class of exact penalty functions and penalty algorithms

Global optimization of polynomial-expressed nonlinear optimal control problems with semidefinite programming relaxation

Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming

The oracle penalty method

An approach to constrained global optimization based on exact penalty functions

A homotopy interior point method for semi-infinite programming problems

On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming

A homotopy method for nonlinear semidefinite programming

Discrete global descent method for discrete global optimization and nonlinear integer programming

A homotopy method based on penalty function for nonlinear semidefinite programming

Similar Documents

A new class of exact penalty functions and penalty algorithms

Global optimization of polynomial-expressed nonlinear optimal control problems with semidefinite programming relaxation

Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming

The oracle penalty method

An approach to constrained global optimization based on exact penalty functions

A homotopy interior point method for semi-infinite programming problems

On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming

A homotopy method for nonlinear semidefinite programming

Discrete global descent method for discrete global optimization and nonlinear integer programming

A homotopy method based on penalty function for nonlinear semidefinite programming