STrustr

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Purpose

Solve optimization problems constrained by a convex feasible region.

sTrustr solves problems of the form



where , , and .

Calling Syntax

Result = sTrustr(Prob, varargin)

Inputs

Prob Problem description structure. The following fields are used:
A Constraint matrix for linear constraints.
b_L Lower bounds on the linear constraints.
b_U Upper bounds on the linear constraints.
c_L Lower bounds on the general constraints.
c_U Upper bounds on the general constraints.
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).
FUNCS.c Name of m-file computing the vector of constraint functions c(x).
FUNCS.dc Name of m-file computing the matrix of constraint normals δc(x)/dx.
optParam Structure with special fields for optimization parameters, see TOMLAB Appendix A.

Fields used are: eps_f, eps_g, eps_c, eps_x, eps_Rank, MaxIter, wait, size_x, size_f, xTol, LowIts, PriLev, method and QN InitMatrix.

PartSep Structure with special fields for partially separable functions, see TOMLAB Appendix A.
varargin Other parameters directly sent to low level routines.

Description of Outputs

Result 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.
c_k Value of constraints at optimum.
H_k Hessian value at optimum.
v_k Lagrange multipliers.
x_0 Starting point.
f_0 Function value at start.
cJac Constraint Jacobian at optimum.
xState State of each variable, described in TOMLAB Appendix A.
Iter Number of iterations.
ExitFlag Flag giving exit status.
Inform Binary code telling type of convergence:

1: Iteration points are close.

2: Projected gradient small.

3: Iteration points are close and projected gradient small.

4: Relative function value reduction low for LowIts iterations.

5: Iteration points are close and relative function value reduction low for LowIts iterations.

6: Projected gradient small and relative function value reduction low for LowIts iterations.

7: Iteration points are close, projected gradient small and relative function value reduction low for LowIts iterations.

8: Too small trust region.

9: Trust region small. Iteration points close.

10: Trust region and projected gradient small.

11: Trust region and projected gradient small, iterations close.

12: Trust region small, Relative f(x) reduction low.

13: Trust region small, Relative f(x) reduction low. Iteration points are close.

14: Trust region small, Relative f(x) reduction low. Projected gradient small.

15: Trust region small, Relative f(x) reduction low. Iteration points close, Projected gradient small.

101: Maximum number of iterations reached.

102: Function value below given estimate.

103: Convergence to saddle point (eigenvalues computed).

Solver Solver used.
SolverAlgorithm Solver algorithm used.
Prob Problem structure used.

Description

The routine sTrustr is a solver for general constrained optimization, which uses a structural trust region algorithm combined with an initial trust region radius algorithm (itrr). The feasible region defined by the constraints must be convex. BFGS or DFP is used for the Quasi-Newton update, if the analytical Hessian is not used. sTrustr calls internal routine itrr.

M-files Used

qpSolve.m, tomSolve.m, iniSolve.m, endSolve.m

See Also

  • conSolve
  • nlpSolve
  • clsSolve