Quickguide QPCON Problem

This page is part of the Quickguide Manual. See Quickguide.

When solving a problem with a quadratic objective and nonlinear constraints TOMLAB automatically supplies objective derivatives (gradient and Hessian) if qpconAssign is used.

The quadratic constrained nonlinear programming problem is defined as:

${\begin{array}{ll}\min \limits _{x}&f(x)={\frac {1}{2}}x^{T}Fx+d^{T}x\\&\\s/t&{\begin{array}{lcccl}x_{L}&\leq &x&\leq &x_{U}\\b_{L}&\leq &Ax&\leq &b_{U}\\c_{L}&\leq &c(x)&\leq &c_{U}\\\end{array}}\end{array}}$

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

The following files define and solve an example problem in TOMLAB.

File: tomlab/quickguide/qpconQG.m, qpconQG_c.m, qpconQG_dc.m, qpcon_d2c.m

c:   Nonlinear constraint vector
dc:  Nonlinear constraint gradient matrix
d2c: The second part of the Hessian to the Lagrangian function for the nonlinear constraints.

The following file illustrates how to solve this QPCON problem in TOMLAB. Also view the m-files specified above for more information.

File: tomlab/quickguide/qpconQG.m

Open the file for viewing, and execute qpconQG in Matlab.

 % qpconQG is a small example problem for defining and solving quadratic
 % nonlinearly constrained programming problems using the TOMLAB format.
 
 Name  = 'QP constrained problem';
 x_0   = ones(10,1);
 x_L   = [];
 x_U   = [];
 A     = ones(8,10);
 for i = 1:8
     A(i,i) = 1/2;
 end
 b_L   = ones(8,1);
 b_U   = ones(8,1);
 c_L   = 4;
 c_U   = 4;
 
 % Objective f = -x'*x + sum(x), assign as quadratic/linear matrix/vector
 
 F     = -2*speye(10);
 d     = ones(10,1);
 
 Prob = qpconAssign(F, d, x_L, x_U, Name, x_0, A, b_L, b_U,...
     'qpconQG_c', 'qpconQG_dc', 'qpconQG_d2c', [], c_L, c_U);
 
 % Run SNOPT as a local solver
 Result = tomRun('snopt', Prob, 1);
 % Result2 = tomRun('minos', Prob, 1);
 % Result3 = tomRun('npsol', Prob, 1);
 % Result4 = tomRun('knitro', Prob, 1);