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

摘要

A new two-part parametric linearization technique is proposed globally to a class ofnonconvex programming problems (NPP). Firstly, a two-part parametric linearization methodis adopted to construct the underestimator of objective and constraint functions, by utilizinga transformation and a parametric linear upper bounding function (LUBF) and a linear lowerbounding function (LLBF) of a natural logarithm function and an exponential function witheas the base, respectively. Then, a sequence of relaxation lower linear programming problems, which areembedded in a branch-and-bound algorithm, are derived in an initial nonconvex programmingproblem. The proposed algorithm is converged to global optimal solution by means of asubsequent solution to a series of linear programming problems. Finally, some examples aregiven to illustrate the feasibility of the presented algorithm.