| Global optimization problems abound in economic modeling, finance, network and transportation, database, chip design, image processing, chemical engineering design and centrol, molecular biology and enviromental engineering. We pay more attention to some special classes of programming problems in the fields of local optimality problems and global optimality problems. Especially in quadratic programming problems and cubic programming problems. The cubic optimization problem has spawned a variety of appli-cations, especially in convex optimization, engineering design and structural optimization. Moreover, research results about cubic optimization problem can be applied to quadratic programming problems, which have been widely studied because of its broad applications, to enrich quadratic programming theory. So, it is very improtant to research cubic pro-gramming problems. In this thesis, we would study some global optimality conditions for the following classes of programming problems:sufficient global optimality conditions for a special cubic programming problem with quadratic constraints, sufficient global opti-mality conditions for a special cubic programming problem with mixed binary constraints and global optimality conditions and optimality methods for cubic programming problem with linear constraints.In the first chapter of this thesis, we introduce the recent developments in global optimization. The sufficient global optimality conditions for a special cubic programming problem with quadratic constraints are discussed in chapter2. In chapter3, the sufficient global optimality conditions for a special cubic programming problem with mixed binary constraints are established. In the forth chapter, we still study the necessary optimality conditions and optimality methods for cubic polynomial optimization problems with linear constraints. Lastly, we also provide some numerical examples to illustrate our global optimality conditions. |
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