init_bound_resect.m

数学优化工具箱

function [limlist, feas_status] = init_bound_resect(xm, Xlist, nbrpoints, beta, m, n, maxdepth, flag)

  feas_status = 1;
  A = sparse(zeros(0,m*n));
  Al = sparse(zeros(0,m*n));
  A_f = sparse(zeros(0,m*n));
  c = sparse(zeros(0,1));
  cl = sparse(zeros(0,1));
  c_f = sparse(zeros(0,1));
  
  A = [];  c = [];
  Al = []; cl = [];
  
  clear K;
  K.q = [];
  K.f = 0;
  K.l = 0;

  x = Xlist(:,1)';
  c_f = 1;
  A_f = [zeros(1,(m-1)*n), x];
  K.f = K.f + 1;
  
  %keyboard;
  
  for j = 1:m-1
    umin(j) = min(xm(j,:));
    umax(j) = max(xm(j,:));
  end
  uminb = max(0,umin-(umax-umin)/5);
  umaxb = umax+(umax-umin)/5;
  
  for i = 1:nbrpoints
    x = Xlist(:,i)';
    Atmp1 = [];  Atmp2 = [];  ctmp1 = [];  ctmp2 = [];
    for j = 1:m-1
      Atmp1(j,(j-1)*n+1:j*n) = -x;
      Atmp1(j,(m-1)*n+1:m*n) = uminb(j)*x;
      ctmp1(j,1) = 0;
      Atmp2(j,(j-1)*n+1:j*n) = x;
      Atmp2(j,(m-1)*n+1:m*n) = -umaxb(j)*x;
      ctmp2(j,1) = 0;
    end
    Al = [Al; Atmp1; Atmp2];
    cl = [cl; ctmp1; ctmp2];
    K.l = K.l + length([ctmp1;ctmp2]);
  end
  
  %keyboard;
  
  Atmp = []; ctmp = [];
  for i = 2:nbrpoints
    x = Xlist(:,i)';
    ctmp(i-1,1) = maxdepth;
    Atmp(i-1,(m-1)*n+1:m*n) = x;
  end
  Al = [Al; Atmp];
  cl = [cl; ctmp];
  K.l = K.l + nbrpoints-1;
  
  %keyboard;
  
  i = 1;
  Atmp = zeros(m,m*n);
  ctmp = zeros(m,1);
  x = Xlist(:,i)';
  u = xm(:,i)';
  ctmp(1,1) = beta;
  for j = 1:m-1
      Atmp(j+1,(j-1)*n+1:j*n) = x;
      ctmp(j+1,1) = u(j);
  end
  A = [A; Atmp];
  c = [c; ctmp];
  K.q = [K.q, m];

  
  for i = 2:nbrpoints
    Atmp = zeros(m,m*n);
    ctmp = zeros(m,1);
    x = Xlist(:,i)';
    u = xm(:,i)';
    Atmp(1,(m-1)*n+1:m*n) = -beta*x;
    for j = 1:m-1
      Atmp(j+1,(j-1)*n+1:j*n) = x;
      Atmp(j+1,(m-1)*n+1:m*n) = -u(j)*x;
    end
    A = [A; Atmp];
    c = [c; ctmp];
    K.q = [K.q, m];
  end

  A = [A_f; Al; A];
  c = [c_f; cl; c];

  limlist = zeros(n+1,2);
  limlist(1,:) = [1,1];
  
  if flag == 1
    pars1.fid = 0;
    pars1.eps = 0;
    [x1,y1,info1] = sedumi(A,0,c,K,pars1);
    if info1.dinf == 1 || info1.numerr == 2
      feas_status = 0;
    end
    limlist(2:n,:) = zeros(n-1,2);
    return;
  end


  for i = 2:n+1
    b = [zeros((m-1)*n,1); Xlist(:,i)];
    pars1 = [];
    pars1.fid = 0;
    pars1.eps = 0;
    [x1,y1,info1] = sedumi(A, -b, c, K, pars1);
    %info1
    limlist(i,1) = b'*y1;
    if info1.dinf == 1 || info1.numerr == 2
    %    keyboard;
      feas_status = 0;
      limlist(2:n,:) = zeros(n-1,2);
      return;
    end

    pars2 = [];
    pars2.fid = 0;
    pars2.eps = 0;
 %   keyboard;
    [x2,y2,info2] = sedumi(A, b, c, K, pars2);
    %info2
    limlist(i,2) = b'*y2; 
    if info2.dinf == 1 || info2.numerr == 2
 %       keyboard;
      feas_status = 0;
      limlist(2:n,:) = zeros(n-1,2);
      return;
    end
  end
  
  
  inrect1old.sllist = [limlist(:,1)',0.001*ones(1,nbrpoints-n-1)];
  inrect1old.sulist = [limlist(:,2)',maxdepth*ones(1,nbrpoints-n-1)];
    
  index2 = n;
  inrect1 = propagateresect(inrect1old, index2, Xlist, nbrpoints, m, n);
  
  clear limlist;
  limlist = [inrect1.sllist', inrect1.sulist'];