Computer Science ›› 2015, Vol. 42 ›› Issue (2): 247-252.doi: 10.11896/j.issn.1002-137X.2015.02.051

Previous Articles     Next Articles

Interval Iterative Algorithm for a Class of Convex Optimization

TANG Min and DENG Guo-qiang   

  • Online:2018-11-14 Published:2018-11-14

Abstract: This paper studied solving method for nonlinear constrained convex optimization and pointed out how to make use of Kuhn-Tucker condition to transfer convex programming to find roots of multivariate nonlinear systems equivalently.Our interval approach for finding optimal solutions can be combined with the principle of interval arithmetic and the modified iterative version given by R.Krawczyk.In the case of a convex programming with differentiable objective and constrained functions,the ability of global optimization can be improved.We illustrated the numerical experiments in contrast to the classical algorithms such as genetic algorithm,pattern search method,simulated annealing method and some built-in facilities of mathematical software packages.The implementation indicates that our method can provide a relative guaranteed bound on the error of the computed value and obtain more global optimal solutions.

Key words: Interval iterative method,Convex programming,Krawczyk operator,Kuhn-Tucker condition

[1] Boyd S P,Vandenberghe L.Convex Optimization[M].Cam-bridge university press,2004
[2] Goldberg D E.Genetic Algorithms in Search,Optimization,& Machine Learning[M].Reading Menlo Park:Addison-wesley,1989
[3] Kirkpatrick S,Vecchi M P.Optimization by simulated annealing[J].Science,1983,220(4598):671-680
[4] Colorni A,Dorigo M,Maniezzo V.Distributed optimization by ant colonies[C]∥Proceedings of the First European Conference on Artificial Life.1991,142:134-142
[5] Hillier F S,Lieberman G J.Introduction to Operations Research(Ninth Edition)[M].北京:清华大学出版社,2010
[6] Moore R E.Interval Arithmetic and Automatic Error Analysisin Digital Computing[D].Stanford:Department of Mathema-tics,Stanford University,1962
[7] Moore R E,Kearfott R B,Cloud M J.Introduction to IntervalAnalysis[M].Society for Industrial & Applied Mathematics,2009
[8] 张建华.基于区间数学的全局优化算法及其应用研究[D].合肥:合肥工业大学,2012
[9] Szlama A,Kalauz K,Heckl I,et al.Solving a separation-network synthesis problem by interval global optimization technique[J].Computers & Chemical Engineering,2013,56:142-154
[10] Mazhoud I,Hadj-Hamou K,Bigeon J,et al.Interval-based global optimization in engineering using model reformulation and constraint propagation[J].Engineering Applications of Artificial Intelligence,2012,25(2):404-417
[11] Markót M C,Fernandez J,Casado L G,et al.New interval me-thods for constrained global optimization[J].Mathematical Programming,2006,106(2):287-318
[12] Karmakar S,Mahato S K,Bhunia A K.Interval oriented multi-section techniques for global optimization[J].Journal of Computational and Applied Mathematics,2009,224(2):476-491
[13] Byrne R P,Bogle I D L.Global optimisation of constrained non-convex programs using reformulation and interval analysis[J].Computers & Chemical Engineering,1999,23(9):1341-1350
[14] Kearfott R B,Dawande M,Du K,et al.Algorithm 737:Intlib—a portable fortran 77 interval standard-function library[J].ACM Transactions on Mathematical Software (TOMS),1995,20(4):447-459
[15] Kearfott R B.Algorithm 763:INTERVAL_ARITHMETIC:A Fortran 90 module for an interval data type[J].ACM Transactions on Mathematical Software (TOMS),1996,22(4):385-392
[16] Schulte M J,Zelov V,Akkas A,et al.The interval-enhancedGNU Fortran compiler[J].Reliable Computing,1999,5(3):311-322
[17] 《运筹学》教材编写组.运筹学(第四版)[M].北京:清华大学出版社,2012
[18] Moore R E.A test for existence of solutions to nonlinear systems[J].SIAM Journal on Numerical Analysis,1977,14(4):611-615
[19] Rump S M.Verification methods for dense and sparse systems of equations[S].Topics in validated computations,1994:63-136
[20] Tsai L W,Morgan A P.Solving the kinematics of the most general six-and five-degree-of-freedom manipulators by continuation methods[J].Journal of Mechanisms,Transmissions and Automation in Design,1985,107(2):189-200

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!