Design and Implementation of Optimization Software

ISBN-13: 9789400999374 / Angielski / Miękka / 2011 / 565 str.

H. J. Greenberg

Opis

This proceedings contains tutorials presented at the NATO Advanced Study Institute on Design and Implementation of Optimiz ation Software (Urbino, Italy, 20 June - 2 July, 1977) organized by the Committee on Algorithms (COAL) of the Mathematical Program ming Society. The authors are to be congratulated on their clear expositions plus their prompt cooperation. We were especially fortunate to have had two of the first pioneers in designing mathematical programming systems: W. Orchard-Hays and E. M. L. Beale. Surveying the contents the reader will find that the papers fall into three categories which we can roughly designate by: linear programming, extensions of linear programming, and non linear programming. In the first category on linear programming, the three back ground papers by W. Orchard-Hays capture a historical perspective through the scope of modern systems, while T. J. Dekker's paper provides background in numerical methods used in optimization software. One area neglected by most previous mathematical pro gramming symposia is the information structure employed to mani pulate large volumes of data. The tutorial on matricial packing by H. J. Greenberg includes modern structures, including recent suggestions by J. Kalan and D. Rarick; another tutorial on pivot selection describes the vast range of tactics that have evolved, aimed at reducing computational effort with the strategy of the simplex method."

Spis treści

History of mathematical programming systems.- Scope of mathematical programming software.- Anatomy of a mathematical programming system.- Elements of numerical linear algebra.- A tutorial on matricial packing.- Pivot selection tactics.- An interactive query system for MPS solution information.- Modeling and solving network problems.- Integer programming codes.- Some considerations in using branch-and bound codes.- Quadratic programming.- Nonlinear programming using a general mathematical programming system.- The design and implementation of software for unconstrained optimization.- The GRG method for nonlinear programming.- Generalized reduced gradient software for linearly and nonlinearly constrained problems.- The ALGOL 60 procedure minifun for solving non-linear optimization problems.- An accelerated conjugate gradient algorithm.- Global optima without convexity.- Computational aspects of geometric programming.- A proposal for the classification and documentation of test problems in the field of nonlinear programming.- Guidelines for reporting computational experiments in mathematical programming.- COAL session summary.- List of participants.