SYSTEMS OPTIMIZATION LABORATORY DEPARTMENT OF MANAGEMENT SCIENCE AND ENGINEERING STANFORD UNIVERSITY STANFORD, CALIFORNIA, USA MINOS 5.51 USER’S GUIDE by Bruce A. Murtagh† and Michael A. Saunders‡ TECHNICAL REPORT SOL 83-20R December 1983 Revised September 23, 2003 Copyright c 1983–2002 Stanford University †Graduate School of Management, Macquarie University, Sydney, NSW, Australia (
[email protected]). ‡Dept of Management Science and Engineering, Terman Building, Stanford University, Stanford, CA 94305-4026, USA (
[email protected]). Research and reproduction of this report were supported by the Department of Energy contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; National Science Foundation grants MCS- 7926009, ECS-8012974 and CCR-9988205; the Office of Naval Research contracts N00014-75-C-0267 and N00014-02-1-0076; and the Army Research Office contract DAAG29-81-K-0156. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the above sponsors. Reproduction in whole or in part is permitted for any purposes of the United States Government. ii Contents Preface to MINOS 5.51 vii Preface to MINOS 5.0 xv 1 Introduction 3 1.1 LinearProgramming .................................. 4 1.2 Problems with a Nonlinear Objective . 5 1.3 Problems with Nonlinear Constraints . ..... 7 1.4 ProblemFormulation................................. ... 9 1.5 Restrictions....................................... 10 1.6 Storage .......................................... 10 1.7 Files............................................ 11 1.8 InputDataFlow ...................................... 11 1.9 MultipleSPECSFiles .................................. 12 1.10 Internal Modifications . 13 2 User-written Subroutines 15 2.1 Subroutine funobj . 15 2.2 Subroutine funcon . 17 2.3 Constant Jacobian Elements .