运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2007年
1期
1-15
,共15页
运筹学%全局最优解%凹极小%反凸规划%凸化%凹化
運籌學%全跼最優解%凹極小%反凸規劃%凸化%凹化
운주학%전국최우해%요겁소%반철규화%철화%요화
Operations research%global optimal solution%concave minimization%reverse convex programming problem%convexification%concavification
首先将一个具有多个约束的规划问题转化为一个只有一个约束的规划问题,然后通过利用这个单约束的规划问题,对原来的多约束规划问题提出了一些凸化、凹化的方法,这样这些多约束的规划问题可以被转化为一些凹规划、反凸规划问题.最后,还证明了得到的凹规划和反凸规划的全局最优解就是原问题的近似全局最优解.
首先將一箇具有多箇約束的規劃問題轉化為一箇隻有一箇約束的規劃問題,然後通過利用這箇單約束的規劃問題,對原來的多約束規劃問題提齣瞭一些凸化、凹化的方法,這樣這些多約束的規劃問題可以被轉化為一些凹規劃、反凸規劃問題.最後,還證明瞭得到的凹規劃和反凸規劃的全跼最優解就是原問題的近似全跼最優解.
수선장일개구유다개약속적규화문제전화위일개지유일개약속적규화문제,연후통과이용저개단약속적규화문제,대원래적다약속규화문제제출료일사철화、요화적방법,저양저사다약속적규화문제가이피전화위일사요규화、반철규화문제.최후,환증명료득도적요규화화반철규화적전국최우해취시원문제적근사전국최우해.
Firstly, convert a programming problem with multiple constraints into a programming problem with single constraint. Secondly, several convexification and concavification transformations for the constrained problem with strictly monotone constraint functions are proposed according to the transformed problem with single constraint, then this constrained programming problem can be converted into a concave minimization or a reverse convex programming problem. Finally, prove that any global optimal solution of the converted concave minimization problem or reverse convex programming problem obtained by the existing algorithms is an approximate global optimal solution of the original problem.
