% m23_fminunc.m - minimisation of m22.m function using Matlab's fminunc

  function m23()
  x = [-3:.1:3]; y = x;
  [xx,yy] = meshgrid(x,y);
  ff = xx.^2+yy.^2+yy.*sin(xx)-sin(2*yy);
  hold off, contour(xx,yy,ff,15)          % contour plot
  colorbar, grid on, hold on
  LW = 'linewidth'; MS = 'markersize';
  plot(-.2714,.5635,'.k',MS,30)           % the solution
  x = input('initial x? ');
  y = input('initial y? ');
  xold = x; yold = y;
  X = fminunc(@f,[x;y])                   % minimisation

  function f = f(X)                       % compute function
    x = X(1), y = X(2)
    f = x.^2+y.^2+y.*sin(x)-sin(2*y);
    plot([xold x],[yold y],'-r',LW,1.2)   % plot line to current point
    plot(x,y,'.r',MS,15)                  % plot current point
    disp(' '), pause
    xold = x; yold = y;
  end

  end