1) firstly, the theory, algorithm and convergence of trust region method for cone model are proposed, and the adaptive properties, nonmonotonic processing and interpolation properties of this kind of method are discussed.
2) Firstly, a numerical correlation quasi-Newton method for ill-conditioned optimization problems is proposed, and its nonlinear modulation index and convergence properties are studied.
3) According to the nonmonotonic optimization work of Grippo et al., nonmonotonic inexact line search, nonmonotonic trust region method, nonmonotonic nonsmooth optimization, nonmonotonic complementary algorithm, nonmonotonic general line search method with mandatory function and so on are systematically studied.
4) In the field of nonsmooth optimization, generalized SQP method, generalized Newton method, DC minimization problem, cluster method and trust region method are systematically studied.
Published more than 70 academic papers in core magazines at home and abroad, most of which were published in SCI and EI magazines; Co-published 4 monographs, translated into 1, among which Introduction to Generalized Inverse Matrix (Jiangsu Science and Technology Publishing House, 1990, co-authored with Professor He Xuchu) is one of the earliest monographs on generalized inverse theory and calculation in China, and won the second prize of excellent scientific and technological books in East China; Optimization Theory and Method (Science Press, 1997, co-authored with Professor Yuan Yaxiang) systematically discusses the theory and algorithm of unconstrained, constrained and nonsmooth optimization, including the recent main research results, which has great influence at home and abroad. It is one of the main textbooks for graduate students in domestic universities, and won the "Jiangsu Excellent Postgraduate Course Textbook Award" in 2002. Science Press has printed six times in 1997, 1999, 200 1, 2003, 2004 and 2005. The book Optimization Theory and Algorithm (edited by Professor Yuan Yaxiang in 2005) was recently published by Springer Press, an internationally renowned publishing house. The Optimization Method (Higher Education Press, 2004) is one of the series of information and computing science majors in national colleges and universities compiled by the editorial board of information and computing science majors of the Ministry of Education, and it is the research result of the tenth five-year national planning project of educational science. He has presided over and participated in general projects of the National Natural Science Foundation, key projects and international cooperation research projects of the National Natural Science Foundation, Sino-Italian scientific and technological cooperation projects of the Ministry of Science and Technology, scientific research projects of returned overseas students of the Ministry of Education, doctoral fund projects of the Ministry of Education, international cooperation projects of the Ministry of Science and Technology of Brazil, scientific research projects of the Science and Technology Department of Jiangsu Province and the Education Department of Jiangsu Province. He has presided over many large-scale international and domestic academic conferences in the field of computational mathematics and optimization, such as 1999 Nanjing International Conference on Optimization and Numerical Algebra (Nanjing, 1999.9.25 -29) and the Second International Conference on Optimization and Control and Its Application (Huangshan, China, August 2002 18-22). Seventh National Annual Conference on Computational Mathematics (2003. 10. 18-23, Nanjing Normal University), 2005' Nanjing International Conference on Scientific Computing (4-8 June 2005, Nanjing, China), etc. And participate in other international academic conferences organized at home and abroad. .
Won the Jiangsu Science and Technology Progress Award twice (1984,1988); Excellent postgraduate courses in Jiangsu province in 2002: optimization theory and method; Because of his outstanding achievements in teaching and scientific research after returning to China, he was awarded the honorary title of advanced individual by the Overseas Chinese Affairs Office and the All-China Federation of Returned Overseas Chinese at the Seventh National Congress of Returned Overseas Chinese and Their Families in July 2004.