Randomized Algorithms Control Toolbox Code

function robust_feas = rob_feas(varargin)
%ROB_FEAS find a feasible solution in probabilistic sense for robust problem
%
% robust_feas = rob_feas(hFunc, hGrad, x0)
% robust_feas = rob_feas(hFunc, hGrad, x0, param1, param2, ...)
% robust_feas = rob_feas(hFunc, hGrad, x0, options)
%
% find a vector solution x for common function in form
% f(x, Delta) <= 0 forall Delta \in Delta
% where Q0, Q1, ... are symmetric matrices or handles to 
% user-defined functions with uncertain matrices

% $Id$

if nargin == 3 % (hFunc, hGrad, x0)
  hFunc = varargin{1};
  hGrad = varargin{2};
  x0 = varargin{3};
  options = [];
elseif nargin == 4 % (hFunc, hGrad, x0, options)
  hFunc = varargin{1};
  hGrad = varargin{2};
  x0 = varargin{3};
  options = varargin{4};
else
  error(['RACT:rob_feas:InputSize', ['Incorrect number of arguments: ' num2str(nargin)]]);
end

% validate options
options = valfeasopt(options);

if ~isa(hFunc, 'function_handle')
  error(['RACT:rob_feas:InputType', 'First parameter hFunc should be function handle!']);
end
if ~isa(hGrad, 'function_handle')
  error(['RACT:rob_feas:InputType', 'Second parameter hGrad should be function handle!']);
end

% initial point
x = x0;

Nin = ceil(log(1/options.delta)/log(1/(1 - options.eps)));
FEAS = 0; % constant for feasibility

for k=1:options.Nout
  % cast probabilistic oracle
  if ~(k==1)
    [feasible, Ninter, Delta_viol] = poracle(hFunc, x, Nin, 'cont');
  else
    [feasible, Ninter, Delta_viol] = poracle(hFunc, x, Nin, 'init');
  end
  disp([num2str(k), '-th oracle casted, interrupted on ' num2str(Ninter) ' iteration (max ', num2str(Nin),').']);
  if feasible
    % solution considered to be found with some epsilon and delta
    robust_feas = x;
    return;
  else
    % violation sample found
    % TODO can be speeded up by prefetching type of algorithm
    switch options.method
      case 'grad'
        x = updgrad(hFunc, hGrad, x, Delta_viol, options);
      case 'ell'
        x = updell(hFunc, hGrad, x, Delta_viol, options);
      case 'cutplane'
        x = updcp(hFunc, hGrad, x, Delta_viol, options);
    end
%    [x.', 0, feval(hFunc, 0, Delta_viol, x, 1)]
  end
end

robust_feas = x;
%warning('RACT:rob_feas:NoSolution', 'No feasible solution found.');
warning('No feasible solution found.');