SOL LPOPT
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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 Section 3.4.2 for information on how to use LPOPT with TOMLAB.
Purpose
lpopt solves dense linear optimization problems defined as
If isempty(c) (or all(c==0), then a feasible point problem is solved (FP). Otherwise a standard linear programming problem is solved (LP)
Calling Syntax
[Inform, Iter, iState, Ax, cLamda, Obj, x] = lpopt(A, bl, bu, c, Warm, x, iState, SpecsFile, PrintFile, SummFile, PriLev, optPar );
Description of Inputs
| The following fields are used: | |
|---|---|
| A | Constraint matrix, m x n (DENSE). |
| bl | Lower bounds on (x,Ax), m+n x 1 vector (DENSE). |
| bu | Upper bounds on (x,Ax), m+n x 1 vector (DENSE). |
| c | Linear objective function cost coeffs, n x 1 (DENSE). If length(c) < n, setting c(1:n)=0; |
| Warm | If Warm > 0, then warm start, otherwise cold Start. Default 0. If warm start, then x and iState must be set properly. Normally the values from last call to lpopt are used. |
| x | Initial estimate of solution vector x. (DENSE) If length(x) ¡ n, the rest of the elements in x are set to 0. |
| iState | Working set (if Warm start) (n+m) x 1 (DENSE) If length(iState) ¡ n+m, setting iState(1:n+m)=0;
iState(i)=0: Corresponding constraint not in the initial QP working set. iState(i)=1: Inequality constraint at its lower bound in QP working set. iState(i)=2: Inequality constraint at its upper bound in QP working set. iState(i)=3: Equality constraint in the initial QP working set,bl(i)==bu(i). |
| SpecsFile | Name of the OPTIONS 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 | Print level in the lpopt MEX-interface.
= 0 Silent. = 1 Summary information. = 2 More detailed information. if isempty(PriLev), set as 0. |
| optPar | Vector with optimization parameters overriding defaults and the optionally specified SPECS file. If length(optPar) ¡ 62, lpopt sets the rest of the values to missing value (-999). |
Description of Outputs
| The following fields are used: | |
|---|---|
| Inform | Result of LPOPT run.
0 = Optimal solution with unique minimizer found. 1 = A dead point was reached. 2 = The solution appears to be unbounded (or badly scaled). 3 = The constraints could not be satisfied. The problem has no feasible solu- tion. 4 = Too many iterations, in either phase. 5 = The Maximum degrees of freedom is too small. The reduced Hessian must expand if further progress is too be made. 6 = An input parameter was invalid. 7 = The problem type was not recognized. Other = UNKNOWN LPOPT Inform value. |
| Iter | Number of iterations. |
| iState | Status of working set, se input description of iState. |
| Ax | A*x. |
| cLamda | Lagrangian multipliers (dual solution vector) (m x 1 vector). |
| Obj | Objective function value at optimum. |
| x | Solution vector with decision variable values (n x 1 vector). |
