A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems | Zendy

Xue-Gang Zhou | Zendy; Bing-Yuan Cao | Zendy

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A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems

Author(s) -

Xue-Gang Zhou,

Bing-Yuan Cao

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/697321

Subject(s) - bounding overwatch , mathematics , mathematical optimization , linear programming , linear fractional programming , linearization , criss cross algorithm , linear programming relaxation , relaxation (psychology) , branch and bound , global optimization , parametric statistics , function (biology) , transformation (genetics) , sequence (biology) , algorithm , computer science , nonlinear system , psychology , gene , biology , genetics , social psychology , biochemistry , statistics , physics , chemistry , quantum mechanics , artificial intelligence , evolutionary biology

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function with e as the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm

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