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

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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

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