《數值綫性代數和最優化2003(英文版)》主要內容包括：This conference was the 4th of the biennial conferences， after the first one in Qingdao（1997）， the second one in Nanjing（1999） and the third in Dunhuang（2003）. About 80 participants attended this conference. It is my great pleasure and honour that Professor M.J.D. Powell （who supervised my Ph.D. about twenty years ago）， FRS， of University of Cambridge， came and gave the conference＇s first invited lecture. I am also very glad that we had invited speakers such as Binsheng He， Masao Fukushima， Xingsi Li， Qin Ni， Linqun Qi， M. Raydan， E.W. Sachs， Wenyu Sun， T. Terlaky， Chuanlong Wang， Zengxi Wei， Naihua Xiu， Shufang Xu， Jason Zhang， Liansheng Zhang， Shao-liang Zhang， and Zhenyue Zhang， who reported the recent advances in numerical optimization and numerical linear algebra at the conference. Apart from the academic talks at the conference， there were also informal discussions on the developments of optimization and numerical linear algebra， particularly about promotions of international exchanges and collaborations in these two areas. The conference organized a one-day sightseeing tour along the beautiful Li River， which was enjoyed by all the participants。