Local saddle point and a class of convexification methods for nonconvex optimization problems

Tao Li; Yanjun Wang; Zhian Liang; Panos M. Pardalos

doi:10.1007/s10898-006-9090-4

Local saddle point and a class of convexification methods for nonconvex optimization problems

Tao Li
, Yanjun Wang
, Zhian Liang
, Panos M. Pardalos

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

A class of general transformation methods are proposed to convert a nonconvex optimization problem to another equivalent problem. It is shown that under certain assumptions the existence of a local saddle point or local convexity of the Lagrangian function of the equivalent problem (EP) can be guaranteed. Numerical experiments are given to demonstrate the main results geometrically.

Original language	English
Pages (from-to)	405-419
Number of pages	15
Journal	Journal of Global Optimization
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/s10898-006-9090-4
Publication status	Published - Jul 2007
Externally published	Yes

Keywords

Convexification
Local convexity
Local saddle point
Nonconvex optimization

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10.1007/s10898-006-9090-4

Cite this

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title = "Local saddle point and a class of convexification methods for nonconvex optimization problems",

abstract = "A class of general transformation methods are proposed to convert a nonconvex optimization problem to another equivalent problem. It is shown that under certain assumptions the existence of a local saddle point or local convexity of the Lagrangian function of the equivalent problem (EP) can be guaranteed. Numerical experiments are given to demonstrate the main results geometrically.",

keywords = "Convexification, Local convexity, Local saddle point, Nonconvex optimization",

author = "Tao Li and Yanjun Wang and Zhian Liang and Pardalos, \{Panos M.\}",

year = "2007",

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AU - Li, Tao

AU - Wang, Yanjun

AU - Liang, Zhian

AU - Pardalos, Panos M.

PY - 2007/7

Y1 - 2007/7

N2 - A class of general transformation methods are proposed to convert a nonconvex optimization problem to another equivalent problem. It is shown that under certain assumptions the existence of a local saddle point or local convexity of the Lagrangian function of the equivalent problem (EP) can be guaranteed. Numerical experiments are given to demonstrate the main results geometrically.

AB - A class of general transformation methods are proposed to convert a nonconvex optimization problem to another equivalent problem. It is shown that under certain assumptions the existence of a local saddle point or local convexity of the Lagrangian function of the equivalent problem (EP) can be guaranteed. Numerical experiments are given to demonstrate the main results geometrically.

KW - Convexification

KW - Local convexity

KW - Local saddle point

KW - Nonconvex optimization

UR - https://www.scopus.com/pages/publications/34249894170

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DO - 10.1007/s10898-006-9090-4

M3 - Article

AN - SCOPUS:34249894170

SN - 0925-5001

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SP - 405

EP - 419

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 3

ER -

Local saddle point and a class of convexification methods for nonconvex optimization problems

Abstract

Keywords

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