The generalized quadratic programming (GQP) is an important class of global optimization problems with wide applications in the fields of financial management, statistics and design engineering, with multiple local optimal solutions differing from the global solution. Thus, it is very difficult to obtain a global optimal solution for the GQP. Many solution methods were developed for globally solving the GQPs in a special form and the general form. However, these approaches may sometimes provide an infeasible solution, or one far from the true optimum. To overcome these limitations, a monotonic optimization approach is proposed for the GQP. In the approach, the original problem is first converted into an equivalent monotonic optimization problem, whose objective function is just a simple univariate by exploiting the particular features of this problem. Then, a range division and compression approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using monotonic functions, in which such solution is adequately guaranteed to be feasible and to be close to the actual global optimal solution. At last, several numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.
SHEN Peiping
,
LI Weimin
,
TANG Chong
. A Monotonic Optimization Approach for Solving Globally Generalized Quadratic Programming[J]. Science & Technology Review, 2014
, 32(18)
: 58
-61
.
DOI: 10.3981/j.issn.1000-7857.2014.18.009
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