NlpSolve

Purpose

Solve general constrained nonlinear optimization problems.

nlpSolve solves problems of the form

${\begin{array}{cccccc}\min \limits _{x}&f(x)&&&&\\s/t&x_{L}&\leq &x&\leq &x_{U}\\&b_{L}&\leq &Ax&\leq &b_{U}\\&c_{L}&\leq &c(x)&\leq &c_{U}\end{array}}$

where $x,x_{L},x_{U}\in \mathbb {R} ^{n}$ , $c(x),c_{L},c_{U}\in \mathbb {R} ^{m_{1}}$ , $A\in \mathbb {R} ^{m_{2}\times n}$ and $b_{L},b_{U}\in \mathbb {R} ^{m_{2}}$.

Calling Syntax

Result = nlpSolve(Prob, varargin) 
Result = tomRun('nlpSolve', Prob);

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.
	PriLevOpt	Print level: 0 Silent, 1 Final result, 2 Each iteration, short, 3 Each iteration, more info, 4 Matrix update information.
	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.
	FUNCS.d2c	Name of m-file computing the second derivatives of the constraints, weighted by an input Lagrange vector
	NumDiff	How to obtain derivatives (gradient, Hessian).
	ConsDiff	How to obtain the constraint derivative matrix.
	SolverQP	Name of the solver used for QP subproblems. If empty, the default solver is used. See GetSolver.m and tomSolve.m.
	SolverFP	Name of the solver used for FP subproblems. If empty, the default solver is used. See GetSolver.m and tomSolve.m.
	optParam	Structure with special fields for optimization parameters, see TOMLAB Appendix A. Fields used are: eps_g, eps_x, MaxIter, wait, size_x, method, IterPrint, xTol, bTol, cTol, and QN_InitMatrix.
varargin	Other parameters directly sent to low level routines.

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 Table 150.
	bState	State of each linear constraint, described in Table 151.
	cState	State of each general constraint.
	Inform	Type of convergence.
	ExitFlag	Flag giving exit status.
	ExitText	0: Convergence. Small step. Constraints fulfilled. 1: Infeasible problem? 2: Maximal number of iterations reached. 3: No progress in either function value or constraint reduction.
	Inform	1: Iteration points are close. 2: Small search direction 3: Function value below given estimate. Restart with lower fLow if minimum not reached. 4: Projected gradient small. 10: Karush-Kuhn-Tucker conditions fulfilled.
	Iter	Number of iterations.
	Solver	Solver used.
	SolverAlgorithm	Solver algorithm used.
	Prob	Problem structure used.

Description

The routine nlpSolve implements the Filter SQP by Roger Fletcher and Sven Leyffer.

M-files Used

tomSolve.m, ProbCheck.m, iniSolve.m, endSolve.m

See Also

• conSolve
• sTrustr