均衡约束数学规划问题的一种新的约束规格
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摘要
本文研究了均衡约束数学规划(MPEC)问题.利用其弱稳定点,获得了一种新的约束规格–MPEC的伪正规约束规格.用一种简单的方式,证明了该约束规格是介于MPEC-MFCQ(即MPEC,Mangasarian-Fromowitz约束规格)与MPEC-ACQ(即MPEC,Abadie约束规格)之间的约束规格,因此该约束规格也可以导出MPEC问题的M-稳定点.最后通过两个例子,说明了该约束规格与MPEC-MFCQ以及与MPEC-ACQ之间是严格的强弱关系.
This paper considers mathematical programs with equilibrium constraints(MPEC). A new constraint qualification called MPEC-pseudonormality is proposed by weakly stationary. According to a simple way, we prove that MPEC-pseudonormality is between MPEC Mangasarian-Fromovitz constraint qualification(MPEC-MFCQ) and MPEC Abadies constant qulification(MPEC-ACQ). So MPEC-pseudonormality can also derive M-stationary of MPEC.Finally, we state that the relationships among MPEC-pseudonormality, MPEC-MFCQ and MPEC-ACQ are strict.
This paper considers mathematical programs with equilibrium constraints(MPEC). A new constraint qualification called MPEC-pseudonormality is proposed by weakly stationary. According to a simple way, we prove that MPEC-pseudonormality is between MPEC Mangasarian-Fromovitz constraint qualification(MPEC-MFCQ) and MPEC Abadies constant qulification(MPEC-ACQ). So MPEC-pseudonormality can also derive M-stationary of MPEC.Finally, we state that the relationships among MPEC-pseudonormality, MPEC-MFCQ and MPEC-ACQ are strict.
引文
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[13]杜文,黄崇超.求解二层规划问题的遗传算法[J].数学杂志,2005,25(2):167–170.
[2]Outrata J V.Optimality conditions for a class of mathematical programs with equilibrium constraints[J].Math.Ope.Res.,1999,24(3):627–644.
[3]Outrata J V.A generalized mathematical program with equilibrium constraints[J].SIAM J.Control Optim.,2000,38(5):1623–1638.
[4]Scheel H,Scholtes.Mathematical programs with complementarity constraints:stationarity,optimality,and sensitivity[J].Math.Oper.Res.,2000,25(1):1–22.
[5]Flegel M L,Kanzow C.On M-stationary points for mathematical programs with equilibrium constraint[J].J.Math.Anal.Appl.,2005,310(1):286-302.
[6]Ye J.Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraint[J].J.Math.Anal.Appl.,2005,307(1):350–369.
[7]Flegel M L,Kanzow C.Abadie-type constraint qualification for mathematical programs with equilibrium constraints[J].J.Optim.Theory Appl.,2005,124(3):595–614.
[8]Flegel M L,Kanzow C.On the Guignard constraint qualification for mathematical programs with equilibrium constraints[J].Optim.,2005,54(6):517-534.
[9]Bertsekas D P,Nedic A,Ozdaglar A E.Convexity,duality,and lagrange multipliers[M].Cambridge:Massachusett Institute of Techenology,Spring,2001.
[10]Mangasarian O L.Nonlinear programming[M].Philadelphia:Classics Appl Math.10,SIAM,1994.
[11]Ye J J.Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints[J].SIAM J.Optim.,2000,10(4):943–962.
[12]Ye J J,Zhang J.Enhanced Karush-Kuhn-Tucker condition and weaker constraint qualifications[J].Math.Program,2013,10(1):353–381.
[13]杜文,黄崇超.求解二层规划问题的遗传算法[J].数学杂志,2005,25(2):167–170.