A Conic TrustRegion Method for Nonlinearly Constrained Optimization
 Wenyu Sun,
 Yaxiang Yuan
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Trustregion methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadraticbased methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trustregion algorithm for nonlinearly constrained optimization problems. The trustregion subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.
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 Title
 A Conic TrustRegion Method for Nonlinearly Constrained Optimization
 Journal

Annals of Operations Research
Volume 103, Issue 14 , pp 175191
 Cover Date
 20010301
 DOI
 10.1023/A:1012955122229
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 trustregion method
 conic model
 constrained optimization
 nonlinear programming
 Industry Sectors
 Authors

 Wenyu Sun ^{(1)} ^{(2)}
 Yaxiang Yuan ^{(3)}
 Author Affiliations

 1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China and
 2. Postgraduate Program in Computing Science, Pontificia Universidade Catolica do Parana, Curitiba, PR, 80215901, Brazil
 3. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100080, China