Optimization Toolbox

Example of Converting from constr to fmincon

Old Call to constr

• OPTIONS = foptions;
  OPTIONS(13) = 2;             % Two equality constraints
  OPTIONS(1) = 1;
  OPTIONS(9) = 1;
  A1 = [ 1 4 -3]; b1 = 2;
  A2 = [ 2 5 0]; b2 = 9;
  x0 = [1; .5; .8];
  LB = []; UB = [];
  [X,OPTIONS,LAMBDA,HESS] = ...
     constr('myfuncon',x0,OPTIONS,LB,UB,'mygradcon',A1,b1,A2,b2);
  
  % myfuncon.m
  [F, C] = myfuncon(x,A1,b1,A2,b2)
  F = x(1) + 0.0009*x(2)^3 + sin(x(3));
  
  C(1,1) = A1*x-b;             % Equality linear constraint
  C(2,1) = 3*x(1)^2-1;         % Equality nonlinear constraint
  
  C(3,1) = A2*x-b2;            % Inequality linear constraint
  C(4,1) = 7*sin(x(2))-1;      % Inequality nonlinear constraint
  
  % mygradcon.m
  [G, DC] = mygradcon(x,alpha)
  G = [1;                       % Gradient of the objective
       3*0.0009*x(2)^2;
       cos(x(3))];
  
  DC(:,1) = A1';                % Gradient of the constraints
  DC(:,2) = [6*x(1); 0; 0];
  DC(:,3) = A2';
  DC(:,4) = [0; 7*cos(x(2)); 0];
  

New Call to fmincon

• OPTIONS = optimset(...
     'Display', 'iter', ...
     'GradCheck', 'on', ... % Check gradients.
     'GradObj', 'on', ...   % Gradient of objective is provided.
     'GradConstr', 'on');   % Gradient of constraints is provided.
  
  A1 = [ 1 4 -3]; b1 = 2;   % Linear equalities
  A2 = [ 2 5 0]; b2 = 9;    % Linear inequalities
  
  x0 = [1; .5; .8];
  LB = []; UB = [];
  [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = ...
     fmincon(@myfun,x0,A2,b2,A1,b1,LB,UB,@mycon,OPTIONS);
  
  % myfun.m
  function [F,G] = myfun(x)
  F = x(1) + 0.0009*x(2)^3 + sin(x(3));
  G = [1; 
       3*0.0009*x(2)^2;
       cos(x(3))];
  
  % mycon.m
  function [C,Ceq,DC,DCeq]= mycon(x)
  Ceq(1,1) = 3*x(1)^2-1;         % Equality nonlinear constraint
  C(1,1) = 7*sin(x(2))-1;        % Inequality nonlinear constraint
  DCeq(:,1) = [6*x(1); 0; 0];    % Gradient of equality 
                                 %    nonlinear constraint
  DC(:,1) = [0; 7*cos(x(2)); 0]; % Gradient of inequality 
                                 %    nonlinear constraint
  

New Calling Sequences

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