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

Abstract

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.