In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rat...In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.展开更多
Because of its importance in optimization theory,the concept of convexity has been generalized in various ways.With these generalizations,to seek some practical criteria for them is especially important.In this paper,...Because of its importance in optimization theory,the concept of convexity has been generalized in various ways.With these generalizations,to seek some practical criteria for them is especially important.In this paper,some criteria are developed for semi-prequasi-invexity,which includes prequasi-invexity as the special case.Mutual characterizations among semi-prequasi-invex functions,strictly semi-prequasi-invex functions,and strongly semi-prequasi-invex functions are presented.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.10871226,11001247 and 61179041)Natural Science Foundation of Zhejiang Province(Grant No.Y6100096)
文摘In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.71101088,71003057,71171129the National Social Science Foundation of China under Grant No.11&ZD169+3 种基金the Shanghai Municipal Natural Science Foundation under Grant Nos.10ZR1413200,10190502500,11510501900,12ZR1412800the China Postdoctoral Science Foundation under Grant Nos.2011M500077,2012T50442the Science Foundation of Ministry of Education of China under Grant No.10YJC630087the Doctoral Fundof Ministry of Education of China under Grant No.20113121120002
文摘Because of its importance in optimization theory,the concept of convexity has been generalized in various ways.With these generalizations,to seek some practical criteria for them is especially important.In this paper,some criteria are developed for semi-prequasi-invexity,which includes prequasi-invexity as the special case.Mutual characterizations among semi-prequasi-invex functions,strictly semi-prequasi-invex functions,and strongly semi-prequasi-invex functions are presented.
