Tomlab /Snopt1
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USER'S GUIDE FOR TOMLAB /SNOPT1 Kenneth Holmstr¨om2, Anders O. G¨oran3 and Marcus M. Edvall4 February 13, 2008 ∗More information available at the TOMLAB home page: http://tomopt.com. E-mail: [email protected]. yProfessor in Optimization, M¨alardalenUniversity, Department of Mathematics and Physics, P.O. Box 883, SE-721 23 V¨aster˚as, Sweden, [email protected]. zTomlab Optimization AB, V¨aster˚asTechnology Park, Trefasgatan 4, SE-721 30 V¨aster˚as,Sweden, [email protected]. xTomlab Optimization Inc., 855 Beech St #121, San Diego, CA, USA, [email protected]. 1 Contents Contents 2 1 Introduction 6 1.1 Overview..................................................6 1.2 Contents of this Manual..........................................6 1.3 Prerequisites................................................6 2 Using the Matlab Interface 7 3 TOMLAB /SNOPT Solver Reference8 3.1 MINOS...................................................9 3.1.1 Direct Solver Call.........................................9 3.1.2 Using TOMLAB.......................................... 15 3.1.3 optPar................................................ 19 3.2 LP-MINOS................................................. 22 3.2.1 Using TOMLAB.......................................... 22 3.2.2 optPar................................................ 26 3.3 QP-MINOS................................................. 28 3.3.1 Using TOMLAB.......................................... 28 3.3.2 optPar................................................ 32 3.4 LPOPT................................................... 35 3.4.1 Direct Solver Call......................................... 35 3.4.2 Using TOMLAB.......................................... 38 3.4.3 optPar................................................ 41 3.5 QPOPT................................................... 42 3.5.1 Direct Solver Call......................................... 42 3.5.2 Using TOMLAB.......................................... 46 3.5.3 optPar................................................ 50 3.6 SNOPT................................................... 51 3.6.1 Direct Solver Call......................................... 51 3.6.2 Using TOMLAB.......................................... 57 3.6.3 optPar................................................ 62 3.7 SQOPT................................................... 66 3.7.1 Direct Solver Call......................................... 66 2 3.7.2 Using TOMLAB.......................................... 71 3.7.3 optPar................................................ 75 4 Using the SNOPT Solvers in TOMLAB 77 4.1 Setting Solver Parameters......................................... 77 4.2 Derivatives for the Solvers......................................... 77 4.3 Solver Output to Files........................................... 78 4.4 Warm Starts for the Solvers........................................ 79 4.5 Memory for the Solvers.......................................... 80 4.6 Parameters in Prob.optParam....................................... 80 5 QPOPT details 82 5.1 Introduction................................................. 82 5.1.1 Overview.............................................. 82 5.1.2 The working set.......................................... 82 5.1.3 The reduced Hessian........................................ 83 5.1.4 Optimality conditions....................................... 83 5.2 Further Details of the Method....................................... 85 5.2.1 Treatment of simple upper and lower bounds.......................... 85 5.2.2 The initial working set....................................... 85 5.2.3 The anti-cycling procedure.................................... 86 5.3 The Options File.............................................. 88 5.3.1 Format of option strings...................................... 88 5.4 Description of the optional parameters.................................. 89 5.5 Optional parameter checklist and default values............................. 93 5.6 The Summary File............................................. 94 5.6.1 Constraint numbering and status................................. 94 5.6.2 The iteration log.......................................... 94 5.6.3 Summary file from the example problem............................. 95 5.7 The Print File................................................ 96 5.7.1 Constraint numbering and status................................. 96 5.7.2 The iteration log.......................................... 96 5.7.3 Printing the solution........................................ 97 5.7.4 Interpreting the printout...................................... 98 6 MINOS details 99 6.1 Introduction................................................. 99 3 6.1.1 Linear Programming........................................ 99 6.1.2 Problems with a Nonlinear Objective............................... 101 6.1.3 Problems with Nonlinear Constraints............................... 103 6.1.4 Problem Formulation....................................... 105 6.1.5 Restrictions............................................. 106 6.2 Solver Options............................................... 107 6.2.1 Options for Linear Programming................................. 107 6.2.2 Options for All Problems..................................... 107 6.2.3 Options for Nonlinear Objectives................................. 113 6.2.4 Options for All Nonlinear problems................................ 113 6.2.5 Options for Nonlinear Constraints................................ 118 6.2.6 Options for Input and Output.................................. 123 6.3 File Output................................................. 125 6.3.1 The PRINT file........................................... 125 6.3.2 The major iteration log...................................... 125 6.3.3 The minor iteration log...................................... 127 6.3.4 Crash statistics........................................... 130 6.3.5 Basis factorization statistics.................................... 130 6.3.6 EXIT conditions.......................................... 132 6.3.7 Solution output........................................... 137 6.3.8 The SUMMARY file........................................ 139 7 SQOPT details 141 7.1 Introduction................................................. 141 7.2 Brief description of the method...................................... 143 7.2.1 Formulation of the problem.................................... 143 7.2.2 The main iteration......................................... 144 7.3 The SPECS file............................................... 146 7.3.1 SPECS File Checklist and Defaults................................ 146 7.3.2 Description of the optional parameters.............................. 148 7.4 File Output................................................. 156 7.4.1 The iteration Log.......................................... 156 7.4.2 Basis Factorization Statistics................................... 158 7.4.3 Crash statistics........................................... 160 7.4.4 EXIT conditions.......................................... 160 7.5 Solution Output.............................................. 163 4 7.5.1 The SUMMARY file........................................ 165 7.6 Algorithmic Details............................................. 167 7.6.1 Overview.............................................. 167 7.6.2 Definition of the working set................................... 167 7.6.3 The main iteration......................................... 168 7.6.4 Miscellaneous............................................ 169 8 SNOPT details 171 8.1 Introduction................................................. 171 8.1.1 Problem types........................................... 171 8.2 Description of the SQP method...................................... 172 8.2.1 Constraints and slack variables.................................. 172 8.2.2 Major iterations.......................................... 172 8.2.3 Minor iterations.......................................... 173 8.2.4 The merit function......................................... 173 8.2.5 Treatment of constraint infeasibilities.............................. 174 8.3 Optional parameters............................................ 175 8.3.1 The SPECS file........................................... 175 8.3.2 SPECS file checklist and defaults................................. 175 8.3.3 Description of the optional parameters.............................. 178 8.4 File Output................................................. 193 8.4.1 The PRINT file........................................... 193 8.4.2 The major iteration log...................................... 193 8.4.3 The minor iteration log...................................... 195 8.4.4 Basis factorization statistics.................................... 197 8.4.5 Crash statistics........................................... 199 8.4.6 EXIT conditions.......................................... 199 8.4.7 Solution output........................................... 206 8.4.8 The SUMMARY file........................................ 208 References 210 5 1 Introduction 1.1 Overview Welcome to the TOMLAB /SNOPT User's Guide. TOMLAB /SNOPT includes a set of solvers and MATLAB embedded interfaces. The solver package includes binaries for the following solvers: MINOS - For large-scale sparse general nonlinear programming problems. LP-MINOS - For large-scale sparse linear programming problems. QP-MINOS - For large-scale sparse quadratic programming problems. LPOPT - For dense linear programming