SOL LPOPT
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 #Using TOMLAB for information on how to use LPOPT with TOMLAB.
Purpose
lpopt solves dense linear optimization problems defined as
where , , and .
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). |
Using TOMLAB
Purpose
lpoptTL solves dense linear optimization problems defined as
where , , and .
Calling Syntax
Using the driver routine tomRun :
Prob = lpAssign( ... ); Result = tomRun('lpopt', Prob ... ); or Prob = ProbCheck( ... ); Result = lpoptTL(Prob);
Call Prob = lpAssign( ... ) or Prob=ProbDef to define the Prob for the second option.
Description of Inputs
Prob, The following fields are used: | |
---|---|
x_L, x_U | Bounds on variables. |
b_L, b_U | Bounds on linear constraints. |
A | Linear constraint matrix. |
QP.c | Linear coefficients in objective function. |
PriLevOpt | Print level. |
WarmStart | If true, use warm start, otherwise cold start. |
SOL.xs | Solution and slacks from previous run. |
SOL.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). |
SOL.SpecsFile | Name of user defined SPECS file, read BEFORE optPar() is used. |
SOL.PrintFile | Name of SOL Print file. Amount and type of printing determined by SPECS parameters or optPar parameters. |
SOL.SummFile | Name of SOL Summary File. |
SOL.optPar | Elements > -999 takes precedence over corresponding TOMLAB params. See Table 50. |
Description of Outputs
Result, The following fields are used: | |
---|---|
Result | The structure with results (see ResultDef.m). |
f_k | Function value at optimum. |
x_k | Solution vector. |
x_0 | Initial solution vector. |
g_k | Gradient c (linear objective). |
xState | State of variables. Free == 0; On lower == 1; On upper == 2; Fixed == 3; |
bState | State of linear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3; |
v_k | Lagrangian multipliers (for bounds + dual solution vector). |
ExitFlag | Exit status from lpopt.m (similar to TOMLAB). |
Inform | LPOPT information parameter.
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. |
rc | Reduced costs. If ninf=0, last m == -v k. |
Iter | Number of iterations. |
FuncEv | Number of function evaluations. |
ConstrEv | Number of constraint evaluations. |
QP.B | Basis vector in TOMLAB QP standard. MinorIter Number of minor iterations. Not Set. Solver Name of the solver (lpopt). |
SolverAlgorithm | Description of the solver. |
SOL.xs | Solution and slack variables. |
SOL.iState | State for variables and constraints in iState. |
optPar
Description
Use missing value (-999 or less), when no change of parameter setting is wanted. No call is then done to internal routines lpprmi, lpprmr and lpprm. The default value will then be used by LPOPT, unless the value is altered in the SPECS file.
Description of Inputs
Table: The following fields are used:
# | SPECS keyword text | Lower | Default | Upper | Comment |
---|---|---|---|---|---|
Printing | |||||
1. | PRINT LEVEL | 0 | 10 | 0,1,5,10,20,30 | |
Convergence Tolerances | |||||
In LPOPT/QPOPT: macheps = 2^{-53} ; eps in Matlab is = 2^{-52} ; | |||||
10. | OPTIMALITY TOLERANCE | > 0 | 1.05E-8 | sqrt(macheps) | |
11. | FEASIBILITY TOLERANCE | > 0 | 1.05E-8 | sqrt(macheps) | |
Other Tolerances | |||||
21. | CRASH TOLERANCE | > 0 | 0.01 | < 1 | |
27. | RANK TOLERANCE | > 0 | 1.11E-14 | 100*macheps | |
30. | ITERATION LIMIT | >0 | max(2000,5(n+m)) | ||
33. | MIN SUM YES (or NO)
IF 1 (MIN SUM YES), minimize the infeasibilities before return. |
0 | 0 | 1 | 1=min infeas. |
36. | FEASIBILITY PHASE ITERATIONS | >0 | max(2000,5(n+m)) | ||
45. | INFINITE STEP SIZE | >0 | 1E20 | ||
Frequencies | |||||
51. | CHECK FREQUENCY | > 0 | 50 | ||
52. | EXPAND FREQUENCY | > 0 | 5 |