TOMLAB Solver Reference: Difference between revisions

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{{Part Of Manual|title=the TOMLAB Manual|link=[[TOMLAB|TOMLAB Manual]]}}
[[Category:Manuals]]
[[Category:Manuals]]
{{cleanup|Clean this article.}}
{{Part Of Manual|title=the TOMLAB Manual|link=[[TOMLAB|TOMLAB Manual]]}}
Detailed descriptions of the TOMLAB  solvers, driver routines and some utilities are given in the following sections. Also see the M-file help for each solver. All solvers except for the TOMLAB  Base Module are described in separate manuals.
Detailed descriptions of the TOMLAB  solvers, driver routines and some utilities are given in the following sections. Also see the M-file help for each solver. All solvers except for the TOMLAB  Base Module are described in separate manuals.


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==Tfmin==
==Tfmin==


Minimize function of one variable. Find miniumum x in [x_L, x_U] for function Func within tolerance xTol.  Solves using Brents minimization algorithm. Reference: "Computer Methods for Mathematical Computations", Forsythe, Malcolm, and Moler, Prentice-Hall, 1976.
Minimize function of one variable. Find miniumum x in [x_L, x_U] for function Func within tolerance xTol.  Solves using Brents minimization algorithm.


*[[Tfmin]]
*[[Tfmin]]
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*[[Tfzero]]
*[[Tfzero]]


====ucSolve====
==ucSolve==
 
'''Purpose'''


Solve unconstrained  nonlinear optimization problems with simple bounds on the variables.
Solve unconstrained  nonlinear optimization problems with simple bounds on the variables.


''ucSolve ''solves problems of the form
*[[ucSolve]]
 
 
<math>
\begin{array}{cccccc}
\min\limits_{x} & f(x) &  &  &  &  \\
s/t & x_{L} & \leq  & x & \leq  & x_{U} \\
\end{array}
</math>
 
 
where <math>x,x_{L},x_{U}\in \MATHSET{R} ^{n}</math>.
 
'''Calling  Syntax'''
 
Result = ucSolve(Prob, varargin)
 
'''Description  of Inputs'''
 
{|
|''Prob''||colspan="2"|Problem description structure. The following fields are used:
|-
|||''x_L''||Lower bounds on the variables.
|-
|||''x_U''||Upper bounds on the variables.
|-
|||''x_0''||Starting point.
|-
|||''FUNCS.f''||Name of m-file computing the objective function ''f ''(''x'').
|-
|||''FUNCS.g''||Name of m-file computing the gradient vector ''g''(''x'').
|-
|||''FUNCS.H''||Name of m-file computing the Hessian matrix ''H ''(''x'').
|-
|||''f_Low''||Lower bound on function value.
|-
|||''Solver.Alg ''||Solver algorithm to be run:
|-
|||||0: Gives default, either Newton or BFGS.
|-
|||||1: Newton with subspace minimization, using SVD.
|-
|||||2: Safeguarded BFGS with inverse Hessian updates (standard).
|-
|||||3: Safeguarded BFGS with Hessian updates.
|-
|||||4: Safeguarded DFP with inverse Hessian updates.
|-
|||||5: Safeguarded DFP with Hessian updates.
|-
|||||6: Fletcher-Reeves CG.
|-
|||||7: Polak-Ribiere CG.
|-
|||||8: Fletcher conjugate descent CG-method.
|-
|||''Solver.Method''||Method used to solve equation system:
|-
|||||0: SVD (default).
|-
|||||1: LU-decomposition.
|-
|||||2: LU-decomposition with pivoting.
|-
|||||3: Matlab built in QR.
|-
|||||4: Matlab inversion.
|-
|||||5: Explicit  inverse.
|-
|||''Solver.Method''||Restart or not for C-G method:
|-
|||||0: Use restart in CG-method each n:th step.
|-
|||||1: Use restart in CG-method each n:th step.
|-
|||''LineParam ''||Structure with line search parameters,  see routine ''LineSearch ''and Table 140.
|-
|||''optParam ''||Structure with special fields for optimization parameters,  see Table 141.
|-
|||||Fields used are: ''eps absf'', ''eps f'', ''eps g'', ''eps x'', ''eps Rank'', ''MaxIter'', ''wait'', ''size x'', ''xTol'', ''size f'', ''LineSearch'', ''LineAlg'', ''xTol'', ''IterPrint ''and ''QN InitMatrix''.
|-
|||''PriLevOpt''||Print level.
|-
|''varargin''||colspan="2"|Other parameters directly sent to low level routines.
|}
 
'''Description  of Outputs'''
 
{|
|''Result''||colspan="2"|Structure with result from optimization.  The following fields are changed:
|-
|||''x_k''||Optimal point.
|-
|||''f_k''||Function value at optimum.
|-
|||''g_k''||Gradient value at optimum.
|-
|||''H_k''||Hessian value at optimum.
|-
|||''B_k''||Quasi-Newton approximation of the Hessian at optimum.
|-
|||''v_k''||Lagrange multipliers.
|-
|||''x_0''||Starting point.
|-
|||''f_0''||Function value at start.
|-
|||''xState''||State of each variable, described in Table 150.
|-
|||''Iter''||Number of iterations.
|-
|||''ExitFlag''||0 if convergence to local min. Otherwise errors.
|-
|||''Inform''||Binary code telling type of convergence:
|-
|||||1: Iteration points are close.
|-
|||||2: Projected gradient small.
|-
|||||4: Relative function value reduction low for ''LowIts ''iterations.
|-
|||||101: Maximum number of iterations reached.
|-
|||||102: Function value below given estimate.
|-
|||||104: Convergence to a saddle point.
|-
|||''Solver''||Solver used.
|-
|||''SolverAlgorithm''||Solver algorithm used.
|-
|||''Prob''||Problem structure used.
|}
 
'''Description'''
 
The solver ''ucSolve ''includes several of the most popular search step methods for unconstrained optimization. The search step methods included in ''ucSolve ''are: the Newton method, the quasi-Newton BFGS and DFP methods, the Fletcher-Reeves and Polak-Ribiere conjugate-gradient method, and the Fletcher conjugate descent method. The quasi-Newton methods may either update the inverse Hessian (standard) or the Hessian itself. The Newton method and the quasi-Newton methods updating the Hessian are using a subspace minimization  technique to handle rank problems, see  Lindstr¨om  \[53\]. The quasi-Newton algorithms also use safe guarding techniques to avoid rank problem in the updated matrix. The line search algorithm in the routine ''LineSearch ''is a modified version of an algorithm by Fletcher \[20\]. Bound constraints are treated as described in Gill, Murray and Wright \[28\]. The accuracy in the line search is critical for the performance of quasi-Newton BFGS and DFP methods and for the CG methods. If the accuracy parameter ''Prob.LineParam.sigma ''is set to the default value 0''.''9, ''ucSolve ''changes it automatically according to:
 
{|
|''Prob.Solver.Alg''||''Prob.LineParam.sigma''
|-
|4,5 (DFP)||0.2
|-
|6,7,8 (CG)||0.01
|}
 
'''M-files  Used'''
 
''ResultDef.m'', ''LineSearch.m'', ''iniSolve.m'', ''tomSolve.m'', ''endSolve.m''
 
'''See Also'''


''clsSolve''
==Additional solvers==
c
====Additional solvers====


Documentation for the following solvers is only available at http://tomopt.com and in the m-file help.
Documentation for the following solvers is only available at http://tomopt.com and in the m-file help.

Latest revision as of 13:30, 17 July 2011

Notice.png

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

Detailed descriptions of the TOMLAB solvers, driver routines and some utilities are given in the following sections. Also see the M-file help for each solver. All solvers except for the TOMLAB Base Module are described in separate manuals.

For a description of solvers called using the MEX-file interface, see the M-file help, e.g. for the MINOS solver minosTL.m. For more details, see the User's Guide for the particular solver.

clsSolve

Solves dense and sparse nonlinear least squares optimization problems with linear inequality and equality con- straints and simple bounds on the variables.

conSolve

Solve general constrained nonlinear optimization problems.

cutPlane

Solve mixed integer linear programming problems (MIP).

DualSolve

Solve linear programming problems when a dual feasible solution is available.

expSolve

Solve exponential fitting problems for given number of terms p.

glbDirect

Solve box-bounded global optimization problems.

glbSolve

Solve box-bounded global optimization problems.

glcCluster

Solve general constrained mixed-integer global optimization problems using a hybrid algorithm.

glcDirect

Solve global mixed-integer nonlinear programming problems.

glcSolve

Solve general constrained mixed-integer global optimization problems.

infLinSolve

Finds a linearly constrained minimax solution of a function of several variables with the use of any suitable TOMLAB solver. The decision variables may be binary or integer.

infSolve

Find a constrained minimax solution with the use of any suitable TOMLAB solver.

linRatSolve

Finds a linearly constrained solution of a function of the ratio of two linear functions with the use of any suitable TOMLAB solver. Binary and integer variables are not supported.

lpSimplex

Solve general linear programming problems.

L1Solve

Find a constrained L1 solution of a function of several variables with the use of any suitable nonlinear TOMLAB solver.

MilpSolve

Solve mixed integer linear programming problems (MILP).

minlpSolve

Branch & Bound algorithm for Mixed-Integer Nonlinear Programming (MINLP) with convex or nonconvex sub problems using NLP relaxation (Formulated as minlp-IP).

mipSolve

Solve mixed integer linear programming problems (MIP).

multiMin

multiMin solves general constrained mixed-integer global optimization problems. It tries to find all local minima by a multi-start method using a suitable nonlinear programming subsolver.

multiMINLP

multiMINLP solves general constrained mixed-integer global nonlinear optimization problems.

nlpSolve

Solve general constrained nonlinear optimization problems.

pdcoTL

pdcoTL solves linearly constrained convex nonlinear optimization problems.

pdscoTL

pdscoTL solves linearly constrained convex nonlinear optimization problems.

qpSolve

Solve general quadratic programming problems.

slsSolve

Find a Sparse Least Squares (sls) solution to a constrained least squares problem with the use of any suitable TOMLAB NLP solver.

sTrustr

Solve optimization problems constrained by a convex feasible region.

Tfmin

Minimize function of one variable. Find miniumum x in [x_L, x_U] for function Func within tolerance xTol. Solves using Brents minimization algorithm.

Tfzero

Tfzero, TOMLAB fzero routine.

ucSolve

Solve unconstrained nonlinear optimization problems with simple bounds on the variables.

Additional solvers

Documentation for the following solvers is only available at http://tomopt.com and in the m-file help.

  • goalSolve - For sparse multi-objective goal attainment problems, with linear and nonlinear constraints.
  • Tlsqr - Solves large, sparse linear least squares problem, as well as unsymmetric linear systems.
  • lsei - For linearly constrained least squares problem with both equality and inequality constraints.
  • Tnnls - Also for linearly constrained least squares problem with both equality and inequality constraints.
  • qld - For convex quadratic programming problem.
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