By M. J. D. Powell (auth.), Ya-xiang Yuan (eds.)
About 60 scientists and scholars attended the ninety six' foreign convention on Nonlinear Programming, which used to be held September 2-5 at Institute of Compu tational arithmetic and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 members have been from outdoor China and 35 from China. The convention was once to have fun the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, college of Cambridge) for his many contributions to nonlinear optimization. On behalf of the chinese language Academy of Sciences, vice chairman Professor Zhi hong Xu attended the hole rite of the convention to precise his hot welcome to all of the members. After the outlet rite, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for moment spinoff approximations in belief zone methods". thirteen different invited lectures on fresh advances of nonlinear programming got throughout the 4 day assembly: "Primal-dual equipment for nonconvex optimization" through M. H. Wright (SIAM President, Bell Labs), "Interior aspect trajectories in semidefinite programming" by means of D. Goldfarb (Columbia collage, Editor-in-Chief for sequence A of Mathe matical Programming), "An method of by-product loose optimization" by way of A.
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Extra info for Advances in Nonlinear Programming: Proceedings of the 96 International Conference on Nonlinear Programming
Recent discussions of primal-dual methods for nonlinear problems are given in [1; 2; 3; 6; 8; 11] . Primal-dual interior methods can be interpreted in several ways; see, for example,  and the recent book  by S. Wright on primal-dual methods A PRIMAL-DUAL INTERIOR METHOD FOR NLP 35 for linear programming. 1) j=l where Il is a positive scalar. Interior methods for constrained optimization, many based on this barrier function, have been the subject of intense research since their revival in 1984; see [17; 23; 28].
626-637. E. , Vol. 257, pp. 311-320. H. Wilkinson (1965), The Algebraic Eigenvalue Problem, Oxford University Press (Oxford). II Invited Lectu res 2 A PRIMAL-DUAL INTERIOR METHOD FOR NONCONVEX NONLINEAR PROGRAMMING David M. com Michael L. edu Margaret H. ), Advances in Nonlinear Programming, 31-56. © 1998 Kluwer Academic Publishers. " "That was the curious incident," remarked Sherlock Holmes. 1 Sir Arthur Conan Doyle, Silver Blaze Abstract: Primal-dual interior methods for nonconvex nonlinear programming have recently been the subject of significant attention from the optimization community.
1), and we have to introduce zero elements into the "El" positions of that expression. 1), and if we apply the procedure of the previous paragraph to the resultant 7 x 7 matrix, retaining s = 2, then the procedure will provide all the new zeros that are required. Three Givens rotations occur, and they are extended from 7x7 to 10xlO matrices by adding three rows and columns of the unit matrix in leading positions. These larger rotation matrices are the ones that are actually used. They do not disturb the band structure that has been achieved in the first three rows and columns of A, because they are of types 20 ADVANCES IN NONLINEAR PROGRAMMING G(9), G(8) and G(7).