American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture
  • JIMO Home
  • This Issue
  • Next Article
    Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty
October  2009, 5(4): 825-834. doi: 10.3934/jimo.2009.5.825

The modified cutting angle method for global minimization of increasing positively homogeneous functions over the unit simplex

Burak Ordin 1,

1. 

Ege University, Faculty of Science, Department of Mathematics, 35100, Bornova, Izmir, Turkey

Received  September 2008 Revised  June 2009 Published  August 2009

The paper deals with a method for global minimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. A new approach for solving the auxiliary problem in the cutting angle method is proposed. In the method, the auxiliary problem is reformulated as a certain combinatorial problem. The modified version of the cutting angle method is also applied for Lipschitz functions that could be expressed as increasing positively homogeneous functions. We report results of numerical experiments which demonstrate that the proposed algorithm is very efficient in the search for a global minimum.
Keywords: global optimization, cutting angle method, dominating subset with minimal weight problem., increasing positively homogeneous function, lipschitz function.
Mathematics Subject Classification: Primary: 90C, 65K; Secondary: 49.
Citation: Burak Ordin. The modified cutting angle method for global minimization of increasing positively homogeneous functions over the unit simplex. Journal of Industrial & Management Optimization, 2009, 5 (4) : 825-834. doi: 10.3934/jimo.2009.5.825
[1]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial & Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485
[2]

Liuyang Yuan, Zhongping Wan, Jingjing Zhang, Bin Sun. A filled function method for solving nonlinear complementarity problem. Journal of Industrial & Management Optimization, 2009, 5 (4) : 911-928. doi: 10.3934/jimo.2009.5.911
[3]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895
[4]

Alessandro Fonda, Rafael Ortega. Positively homogeneous equations in the plane. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 475-482. doi: 10.3934/dcds.2000.6.475
[5]

M. L. Miotto. Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function. Communications on Pure & Applied Analysis, 2010, 9 (1) : 233-248. doi: 10.3934/cpaa.2010.9.233
[6]

Tadeusz Antczak. The $ F $-objective function method for differentiable interval-valued vector optimization problems. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020093
[7]

Anurag Jayswala, Tadeusz Antczakb, Shalini Jha. Second order modified objective function method for twice differentiable vector optimization problems over cone constraints. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 133-145. doi: 10.3934/naco.2019010
[8]

Z.Y. Wu, H.W.J. Lee, F.S. Bai, L.S. Zhang. Quadratic smoothing approximation to $l_1$ exact penalty function in global optimization. Journal of Industrial & Management Optimization, 2005, 1 (4) : 533-547. doi: 10.3934/jimo.2005.1.533
[9]

Jianjun Liu, Min Zeng, Yifan Ge, Changzhi Wu, Xiangyu Wang. Improved Cuckoo Search algorithm for numerical function optimization. Journal of Industrial & Management Optimization, 2020, 16 (1) : 103-115. doi: 10.3934/jimo.2018142
[10]

Dmitri E. Kvasov, Yaroslav D. Sergeyev. Univariate geometric Lipschitz global optimization algorithms. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 69-90. doi: 10.3934/naco.2012.2.69
[11]

Pablo G. Barrientos, Abbas Fakhari, Aliasghar Sarizadeh. Density of fiberwise orbits in minimal iterated function systems on the circle. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3341-3352. doi: 10.3934/dcds.2014.34.3341
[12]

Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew J. Morris. Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Electronic Research Announcements, 2014, 21: 8-18. doi: 10.3934/era.2014.21.8
[13]

Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091
[14]

Zhiyou Wu, Fusheng Bai, Guoquan Li, Yongjian Yang. A new auxiliary function method for systems of nonlinear equations. Journal of Industrial & Management Optimization, 2015, 11 (2) : 345-364. doi: 10.3934/jimo.2015.11.345
[15]

Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 353-362. doi: 10.3934/jimo.2008.4.353
[16]

Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial & Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381
[17]

Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 55-75. doi: 10.3934/era.2015.22.55
[18]

Wen-ling Zhao, Dao-jin Song. A global error bound via the SQP method for constrained optimization problem. Journal of Industrial & Management Optimization, 2007, 3 (4) : 775-781. doi: 10.3934/jimo.2007.3.775
[19]

Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems & Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487
[20]

Virginia Agostiniani, Rolando Magnanini. Symmetries in an overdetermined problem for the Green's function. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 791-800. doi: 10.3934/dcdss.2011.4.791

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (27)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences