TOMLAB OPTIMIZATION ENVIRONMENT: glcAssign

glcAssign

Purpose

For setting up a global mixed-integer programming problem.

Syntax

   Prob = glcAssign(f, x_L, x_U, Name, A, b_L, b_U, ... 
                    c, c_L, c_U, x_0, setupFile, nProblem, ...
                    IntVars, VarWeight, KNAPSACK, fIP, xIP, ...
                    fLowBnd, x_min, x_max, f_opt, x_opt);

Description

glcAssign is a direct way of setting up a global mixed-integer programming (glc) problem in the TOMLAB Quick (TQ) format.

The information is put into the TOMLAB input problem structure Prob.

   Prob = glcAssign( ....)

It is then possible to solve the glc problem using the TOMLAB glc solver glcSolve with the call:

   Result = glcSolve(Prob);

glcAssign also makes the mideva.m file needed for use with MIDEVA and nonlinear solvers.

Problem

        min    f(x),  x in R^n
         x
        s/t   x_L <=   x  <= x_U
              b_L <= A x  <= b_U
              c_L <= c(x) <= c_U

 Linear    equality equations: Set b_L==b_U
 Nonlinear equality equations: Set c_L==c_U

 Fixed     variables:          Set x_L==x_U. Both x_L and x_U must be finite.

 x(IntVars) are integer values, IntVars is an index set, a subset of [1:n].

Input Parameters

 f       Name of objective function f(x)
 x_L     Lower bounds on x, finite bounds must be given!!!
 x_U     Upper bounds on x, finite bounds must be given!!!
 Name    The name of the problem (string)

The rest of the input parameters are optional

 A       The linear constraint matrix 
 b_L     The lower bounds for the linear constraints, b_L <= A*x <= b_U. 
 b_U     The upper bounds for the linear constraints, b_L <= A*x <= b_U. 
 c       Name of constraint function c(x), computing nonlinear constraints
         c(x) must be defined in a function, see e.g. glc_c.m
 c_L     Lower bound vector in nonlinear constraints, c_L<=c(x)<=c_U. 
 c_U     Upper bound vector in nonlinear constraints, c_L<=c(x)<=c_U. 
 x_0     Starting point x (may be empty, not used by glcSolve)

 b_L, b_U, c_L, c_U must either be empty or of full length

 setupFile  The (unique) name as a TOMLAB setup file. If nonempty glcAssign
            will create a executable m-file with this name and the given
            problem defined as the first problem in this file.
            See glc_prob.m, the TOMLAB predefined glc test file.
            If empty, no setupFile is created.
 nProblem   Number of problems to predefine in the setupFile
            Not used if setupFile is empty.
            If empty assumed to be one. Then text are included in the
            setupFile on how to create additional problems.
            If nProblem > 1,
            If empty, no setupFile is created.
--------------------------------------------------------------------------

The following 5 variables are special for MIP problems, and are assigned to the field Prob.MIP.IntVars, etc.

 IntVars    If IntVars is a scalar, then variables 1,...,IntVars are 
            assumed to be integers. 
            If empty, all variables are assumed non-integer 
            If length(IntVars) > 1 ==> length(IntVars) == length(c) must hold,
            Then IntVars(i) ==1 ==> x(i) integer. IntVars(i) ==0 ==> x(i) real.

The following four variables are included (similar to MIP problems), but are not used now by glcSolve:

 VarWeight  Weight for each variable in the variable selection phase.
            A lower value gives higher priority. Setting
            Prob.MIP.VarWeight = c; for knapsack problems improve convergence.
 KNAPSACK   True if a knapsack problem is to be solved, 
            then a knapsack heuristic is used.
 fIP        An upper bound on the IP value wanted. Makes it possible to
            cut branches and avoid node computations.
 xIP        The x-values giving the fIP value.
--------------------------------------------------------------------------
 fLowBnd    A lower bound on the function value at optimum. Only used if
            running the nonlinear TOMLAB solvers with line search
            A good estimate is not critical. Use [] if not known at all.
 x_min      Lower bounds on each x-variable, used for plotting
 x_max      Upper bounds on each x-variable, used for plotting
 f_opt      Optimal function value(s), if known (Stationary points)
 x_opt      The x-values corresponding to the given f_opt, if known.
            If only one f_opt, give x_opt as a 1 by n vector
            If several f_opt values, give x_opt as a length(f_opt) by n matrix
            If adding one extra column n+1 in x_opt, 
            0 indicates min, 1 saddle, 2 indicates max.
            x_opt and f_opt is used in printouts and plots.

conAssign

lcpAssign