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4  TOMLAB /NLPQL Solver Reference

A detailed description of the TOMLAB /NLPQL[1] solver interface is given below. Also see the M-file help for nlpqlTL.m.

4.1  nlpqlTL

Purpose
Solves constrained nonlinear programming problems.

NLPQL solves problems of the form where x,x_L,x_U Rⁿ,  A R^{m₁ × n},  b_L,b_U R^m₁ and c(x), c_L, c_U R^m₂.


Calling Syntax
Prob = conAssign( ... );
Result = tomRun('nlpql',Prob,...);


Description of Inputs

Prob	Problem description structure. The following fields are used:
	A	Linear constraints coefficient matrix.
	x_L, x_U	Bounds on variables.
	b_L, b_U	Bounds on linear constraints.
	c_L, c_U	Bounds on nonlinear constraints. For equality constraints (or fixed variables), set e.g. b_L(k) == b_U(k).
	PriLevOpt	Print level in MEX interface.
	WarmStart	If true, use warm start, otherwise cold start. When using WarmStart the following parameters are required:
	NLPQL.u	Contains the multipliers with respect to the actual iterate stored in the first column of X. The first M locations contain the multipliers of the M nonlinear constraints, the subsequent N locations the multipliers of the lower bounds, and the final N locations the multipliers of the upper bounds. At an optimal solution, all multipliers with respect to inequality constraints should be nonnegative.
	NLPQL.c	On return, C contains the last computed approximation of the Hessian matrix of the Lagrangian function stored in form of an LDL decomposition. C contains the lower triangular factor of an LDL factorization of the final quasi-Newton matrix (without diagonal elements, which are always one). In the driving program, the row dimension of C has to be equal to NMAX.
	NLPQL.d	The elements of the diagonal matrix of the LDL decomposition of the quasi-Newton matrix are stored in the one-dimensional array D.
	NLPQL	Structure with special fields for the NLPQL solver:
	maxfun	The integer variable defines an upper bound for the number of function calls during the line search.
	maxit	Maximum number of outer iterations, where one iteration corresponds to one formulation and solution of the quadratic programming subproblem, or, alternatively, one evaluation of gradients.
	acc	The user has to specify the desired final accuracy (e.g. 1.0e-7). The termination accuracy should not be smaller than the accuracy by which gradients are computed.
	accqp	The tolerance is needed for the QP solver to perform several tests, for example whether optimality conditions are satisfied or whether a number is considered as zero or not. If ACCQP is less or equal to zero, then the machine precision is computed by NLPQL and subsequently multiplied by 1.0e+4.
	PrintFile	Name of NLPQL Print file. Amount and type of printing determined by PriLevOpt.

Description of Outputs

Result	Structure with result from optimization. The following fields are set:
	f_k	Function value at optimum.
	g_k	Gradient of the function.
	x_k	Solution vector.
	x_0	Initial solution vector.
	c_k	Nonlinear constraint residuals.
	cJac	Nonlinear constraint gradients.
	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;
	cState	State of nonlinear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
	ExitFlag	Exit status from NLPQL MEX.
	ExitText	Exit text from NLPQL MEX.
	Inform	NLPQL information parameter.
	FuncEv	Number of function evaluations.
	GradEv	Number of gradient evaluations.
	ConstrEv	Number of constraint evaluations.
	QP.B	Basis vector in TOMLAB QP standard.
	Solver	Name of the solver (NLPQL).
	SolverAlgorithm	Description of the solver.
	NLPQL.act	The logical array indicates constraints, which NLPQL considers to be active at the last computed iterate.
	NLPQL.u	See inputs.
	NLPQL.c	See inputs.
	NLPQL.d	See inputs.

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