SOL MINOS

This page is part of the SOL Manual. See SOL.

Direct Solver Call

A direct solver call is not recommended unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to subsection Using TOMLAB for information on how to use MINOS with TOMLAB.

Purpose

minos solves nonlinear optimization problems defined as

${\begin{array}{ll}\min \limits _{x}&f(x)\\&\\s/t&{\begin{array}{lcccl}&&x&&,\\b_{L}&\leq &Ax&\leq &b_{U}\\&&c(x)&&\\\end{array}}\end{array}}$

where Failed to parse (unknown function "\MATHSET"): {\displaystyle x \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle f(x) \in \MATHSET{R}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{n+m_1+m_2}} and Failed to parse (unknown function "\MATHSET"): {\displaystyle c(x) \in \MATHSET{R}^{m_2}} .

or quadratic optimization problems defined as

${\begin{array}{ll}\min \limits _{x}&f(x)={\frac {1}{2}}x^{T}Fx+c^{T}x\\&\\s/t&{\begin{array}{lcccl}&&x&&,\\b_{L}&\leq &g(x)&\leq &b_{U}\\&&Ax&&\\\end{array}}\end{array}}$

where Failed to parse (unknown function "\MATHSET"): {\displaystyle c, x \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle F \in \MATHSET{R}^{n \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , and Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} .

The full input matrix A has three parts A = [d/dx g(x); A; c'];

Calling Syntax

The file 'funfdf.m' must be defined and contain: function [mode, f, g] = funfdf(x, Prob, mode, nstate) to compute the objective function f and the gradient g at the point x.

The file 'funcdc.m' must be defined and contain: function [mode ,c ,dcS] = funcdc(x, Prob, mode, nstate) to compute the nonlinear constraint value c and the constraint Jacobian dcS for the nonlinear constraints at the point x.

NOTE: The matrix dcS MUST be a SPARSE MATLAB matrix. Do dcS = sparse(dcS); after dcS has been computed.

[hs, xs, pi, rc, Inform, nS, nInf, sInf, Obj, iwCount, gObj, fCon, gCon] = minos(H, A, bl, bu, nnCon, nnObj, 
nnJac, Prob, iObj,  optPar, Warm, hs, xs, pi, nS, SpecsFile, PrintFile,  SummFile, PriLev, ObjAdd,  moremem, 
ProbName );

Description of Inputs

The following fields are used:

Input	Description
H	Matrix n x n in a quadratic programming (QP) problem. DENSE or SPARSE. Leave empty if LP, or NLP problem.
A	Constraint matrix, m x n SPARSE (nonlinear, linear and objective) m > 0 always!!! Define dummy constraint for unconstrained problems.
bl	Lower bounds on (x,g(x),Ax,c').
bu	Upper bounds on (x,g(x),Ax,c'). NOTE! The bl and bu values for the last nonlinear constraint c must have reverse signs and be put in each other places: If cL <= c(x) <= cU , then bl = -cU and bu = -cL . This is because the bounds acts as the constraints on the slack variables for the nonlinear constraints.
nnCon	Number of nonlinear constraints.
nnObj	Number of nonlinear objective variables.
nnJac	Number of nonlinear Jacobian variables.
Prob	Must be a structure. No check is made in the MEX interface. If TOMLAB calls minos, then Prob is the standard TOMLAB problem structure, otherwise the user should set: Prob.P = ProblemNumber, where ProblemNumber is some integer. If the problem is a LP or QP problem (H defined), the user does not have to specify anything else in the structure. For a general nonlinear objective or nonlinear constraints names of two user written routines must be given: funfdf, actual name stored in Prob.FUNCS.fg, with syntax [mode, f, g] = funfdf(x, Prob, mode, nstate). funcdc, actual name stored in Prob.FUNCS.cdc, with syntax [mode, c, dcS] = funcdc(x, Prob, mode, nstate). MINOS is calling the TOMLAB routines nlp fg.m and nlp cdcS.m in the call- back, and they call funfdf and funcdc, respectively. If these fields in Prob are empty (Prob.FUNCS.fg, Prob.FUNCS.cdc), the TOMLAB callback routines calls the usual function routines. Then the Prob struct should be normally defined, and the fields Prob.FUNCS.f, Prob.FUNCS.g, Prob.FUNCS.c, Prob.FUNCS.dc be set in the normal way (e.g. by the routine mFiles.m, or one of the Assign-routines like conAssign.m). If the mode parameter is 0, funfdf should return f, otherwise both f and the gradient vector g. If the mode parameter is 0, funcdc should return c, otherwise both c and dcS. Note that each row in dcS corresponds to a constraint, and that dcS must be a SPARSE matrix. The user could also write his own versions of the routines nlp fg.m and nlp cdcS.m and put them before in the path.
iObj	Says which row of A is a free row containing a linear objective vector c. If there is no such vector, iObj = 0. Otherwise, this row must come after any nonlinear rows, so that nnCon <= iObj <= m.
optPar	Vector with optimization parameters overriding defaults and the optionally specified SPECS file. If using only default options, set optPar as an empty matrix.
Warm	Flag, if true: warm start. Default cold start (if empty). If 'Warm Start' xs, nS and hs must be supplied with correct values.
hs	Basis status of variables + constraints (n+m x 1 vector). State of vari- ables: 0=nonbasic (on bl), 1=nonbasic (on bu) 2=superbasic (between bounds), 3=basic (between bounds).
xs	Initial vector, optionally including m slacks at the end. If warm start, full xs must be supplied.
pi	Lagrangian multipliers for the nnCon nonlinear constraints. If empty, set as 0.
nS	# of superbasics. Only used if calling again with a Warm Start.
SpecsFile	Name of the SPECS input parameter file, see TOMLAB Guide.
PrintFile	Name of the Print file. Name includes the path, maximal number of characters = 500.
SummFile	Name of the Summary file. Name includes the path, maximal number of char- acters = 500.
PriLev	Printing level in the minos m-file and minos MEX-interface. = 0 Silent = 1 Summary information = 2 More detailed information
ObjAdd	Constant added to the objective for printing purposes, typically 0.
moremem	Add extra memory for the sparse LU, might speed up the optimization. 1E6 is 10MB of memory. If empty, set as 0.
ProbName	Name of the problem. ¡=100 characters are used in the MEX interface. In the MINOS solver the first 8 characters are used in the printed solution and in some routines that output BASIS files. Blank is OK.

Description of Outputs

The following fields are used:

Output	Description
hs	Basis status of variables + constraints (n+m x 1 vector). State of vari- ables: 0=nonbasic (on bl), 1=nonbasic (on bu) 2=superbasic (between bounds), 3=basic (between bounds). Basic and superbasic variables may be outside their bounds by as much as the Feasibility tolerance. Note that if scaling is specified, the Feasibility tolerance applies to the variables of the scaled problem. In this case, the variables of the original problem may be as much as 0.1 outside their bounds, but this is unlikely unless the problem is very badly scaled. Check the "Primal infeasibility" printed after the EXIT message. Very occasionally some nonbasic variables may be outside their bounds by as much as the Feasibility tolerance, and there may be some nonbasics for which xn(j) lies strictly between its bounds. If ninf > 0, some basic and superbasic variables may be outside their bounds by an arbitrary amount (bounded by sinf if scaling was not used).
xs	Solution vector (n+m by 1) with n decision variable values together with the m slack variables.
pi	Lagrangian multipliers (dual solution vector) (m x 1 vector)
rc	Vector of reduced costs, g - ( A I )Tp, where g is the gradient of the objective function if xn is feasible, or the gradient of the Phase-1 objective otherwise. If ninf = 0, the last m entries are -p. Reduced costs vector is of n+m length. Inform||Result of MINOS run. 0 Optimal solution found. 1 The problem is infeasible. 2 The problem is unbounded (or badly scaled). 3 Too many iterations. 4 Apparent stall. The solution has not changed for a large number of iterations (e.g. 1000). 5 The Superbasics limit is too small. 6 User requested termination (by returning bad value). 7 Gradient seems to be giving incorrect derivatives. 8 Jacobian seems to be giving incorrect derivatives. 9 The current point cannot be improved. 10 Numerical error in trying to satisfy the linear constraints (or the linearized nonlinear constraints). The basis is very ill-conditioned. 11 Cannot find a superbasic to replace a basic variable. 12 Basis factorization requested twice in a row. Should probably be treated as inform = 9. 13 Near-optimal solution found. Should probably be treated as inform = 9. 20 Not enough storage for the basis factorization. 21 Error in basis package. 22 The basis is singular after several attempts to factorize it (and add slacks where necessary). 30 An OLD BASIS file had dimensions that did not match the current problem. 32 System error. Wrong number of basic variables. 40 Fatal errors in the MPS file. 41 Not enough storage to read the MPS file. 42 Not enough storage to solve the problem.
nS	# of superbasics.
nInf	Number of infeasibilities.
sInf	Sum of infeasibilities.
Obj	Objective function value at optimum.
iwCount	Number of iterations (major and minor), function and constraint calls.
gObj	Gradient of the nonlinear objective.
fCon	Nonlinear constraint vector.
gCon	Gradient vector (non-zeros) of the nonlinear constraint vector.