Acta mathematica scientia,Series A ›› 2002, Vol. 22 ›› Issue (4): 548-556.
• Articles • Previous Articles Next Articles
GAO Yan
Online:
Published:
Supported by:
上海理工大学基金资助
Abstract:
将犚狀空间中两个凸紧集的Ｄｅｍｙａｎｏｖ差推广到犚犿×狀空间．借助于这种差，建立了Ｃｌａｒｋｅ广义Ｊａｃｏｂｉ与拟微分的关系，从而给出了利用拟微分计算Ｃｌａｒｋｅ广义Ｊａｃｏｂｉ的方法．对于两个有限点集凸包给出了它们Ｄｅｍｙａｎｏｖ差的具体表达式．最后讨论了在求解非光滑方程组中的应用．
Key words: 非光滑优化；非光滑方程组；Ｃｌａｒｋｅ广义Ｊａｃｏｂｉ；拟微分
CLC Number:
GAO Yan. Difference for Two Convex Compact Sets and the Relation Between Clarke Generalized Jacobi and Quasidifferential[J].Acta mathematica scientia,Series A, 2002, 22(4): 548-556.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2002/V22/I4/548
［１］ ＤｅｍｙａｎｏｖＶＦ．ＯｎａｒｅｌａｔｉｏｎｂｅｔｗｅｅｎｔｈｅＣｌａｒｋｅｓｕｂｄｉｆｆｅｒｅｎｔｉａｌａｎｄｑｕａｓｉｄｉｆｆｅｒｅｎｔｉａｌ．ＶｅｓｔｎｉｋＬｅｎｉｎｇｒａｄＵｎｉｖｅｒｓｉ ｔｙ，１９８１，１３：１８３－１８９ ［２］ Ｄｅｍｙａｎｏｖ Ｖ Ｆ，ＳｕｔｔｉＧ．ＲｅｐｒｅｓｅｎｔａｔｉｏｎｏｆｔｈｅＣｌａｒｋｅｓｕｂｄｉｆｆｅｒｅｎｔｉａｌｆｏｒａｒｅｇｕｌａｒｑｕａｓｉｄｉｆｆｅｒｅｎｔｉａｂｌｅｆｕｎｃｔｉｏｎ． ＪｏｕｒｎａｌｏｆＯｐｔｉｍｉｚａｔｉｏｎＴｈｅｏｒｙａｎｄＡｐｐｌｉｃａｔｉｏｎｓ，１９９５，８７（３）：５５３－５６１ ［３］ ＲｕｂｉｎｏｖＡ Ｍ．Ｄｉｆｆｅｒｅｎｃｅｓｏｆｃｏｎｖｅｘｃｏｍｐａｃｔｓｅｔｓａｎｄｔｈｅｉｒａｐｐｌｉｃａｔｉｏｎｓｉｎｎｏｎｓｍｏｏｔｈａｎａｌｙｓｉｓ．ＮｏｎｓｍｏｏｔｈＯｐｔｉｍｉ ｚａｔｉｏｎ ＭｅｔｈｏｄｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓ．Ｓｉｎｇａｐｏｒｅ：ＧｏｒｄｏｎａｎｄＢｒｅａｃｈＳｃｉｅｎｃｅＰｕｂｌｉｓｈｅｒｓ，１９９２．３６６－３７８ ［４］ ＲｕｂｉｎｏｖＡ Ｍ，ＡｋｈｕｎｄｏｖＩＳ．ＤｉｆｆｅｒｅｎｃｅｏｆｃｏｎｖｅｘｃｏｍｐａｃｔｓｅｔｓｉｎｔｈｅｓｅｎｓｅｏｆＤｅｍｙａｎｏｖａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｓｉｎ ｎｏｎｓｍｏｏｔｈａｎａｌｙｓｉｓ．Ｏｐｔｉｍｉｚａｔｉｏｎ，１９９２，２３：１７９－１８８ ［５］ ＧａｏＹ．ＤｅｍｙａｎｏｖｄｉｆｆｅｒｅｎｃｅｏｆｔｗｏｓｅｔｓａｎｄｏｐｔｉｍａｌｉｔｙｃｏｎｄｉｔｉｏｎｓｏｆＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｔｙｐｅｆｏｒｃｏｎｓｔｒａｉｎｅｄｑｕａ ｓｉｄｉｆｆｅｒｅｎｔｉａｂｌｅｏｐｔｉｍｉｚａｔｉｏｎ．ＪｏｕｒｎａｌｏｆＯｐｔｉｍｉｚａｔｉｏｎＴｈｅｏｒｙａｎｄＡｐｐｌｉｃａｔｉｏｎｓ，２０００，１０４：３７７－３９４ ［６］ ＤｅｍｙａｎｏｖＶＦ，ＳｔａｖｒｏｕｌａｋｉｓＧ Ｅ，ＰｏｌｙａｋｏｖａＬ Ｎ，ＰａｎａｇｉｏｔｏｐｏｕｌｏｕｓＰＤ．ＱｕａｓｉｄｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙａｎｄＮｏｎｓｍｏｏｔｈ Ｍｏｄｅｌｌｉｎｇｉｎ Ｍｅｃｈａｎｉｃｓ，ＥｎｇｉｎｅｅｒｉｎｇａｎｄＥｃｏｎｏｍｉｃ．Ｄｏｒｄｅｒｃｈｔ：ＫｌｕｗｅｒＡｃａｄｅｍｉｃＰｕｂｌｉｓｈｅｒｓ，１９９６ ［７］ ＤｅｍｙａｎｏｖＶＦ，ＲｕｂｉｎｏｖＡ Ｍ．ＣｏｎｓｔｒｕｃｔｉｖｅＮｏｎｓｍｏｏｔｈＡｎａｌｙｓｉｓ．Ｂｅｒｌｉｎ：Ｐｅｔｅｒｌａｎｇ，１９９５ ［８］ ＣｌａｒｋｅＦ Ｈ．ＯｐｔｉｍｉｚａｔｉｏｎａｎｄＮｏｎｓｍｏｏｔｈＡｎａｌｙｓｉｓ．Ｎｅｗ Ｙｏｒｋ：Ｊｏｈｎ ＷｉｌｅｙａｎｄＳｏｎ，１９８３ ［９］ 高岩．非光滑优化中的某些理论与算法．大连：大连理工大学博士后出站报告，１９９８ ［１０］ ＧａｏＹ．Ａ ｍｏｄｉｆｉｅｄａｌｇｏｒｉｔｈｍｏｆｆｉｎｄｉｎｇａｎｅｌｅｍｅｎｔｏｆＣｌａｒｋｅｇｅｎｅｒａｌｉｚｅｄｇｒａｄｉｅｎｔｆｏｒａｓｍｏｏｔｈｃｏｍｐｏｓｉｔｉｏｎｏｆｍａｘ ｔｙｐｅｆｕｎｃｔｉｏｎｓ．ＪｏｕｒｎａｌｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ，２０００，１８：５１３－５２０ ［１１］ ＱｉＬ，ＳｕｎＪ．ＡｎｏｎｓｍｏｏｔｈｖｅｒｓｉｏｎｏｆＮｅｗｔｏｎ＇ｓｍｅｔｈｏｄ．ＭａｔｈｅｍａｔｉｃａｌＰｒｏｇｒａｍｍｉｎｇ，１９９３，５８：３５３－３６７
Cited
Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications
The Maximal Dilatation and Boundary Dilatation of Quasi-symmetric Mapping