v2007.09.13 - Convex Optimization
v2007.09.13 - Convex Optimization v2007.09.13 - Convex Optimization
658 APPENDIX F. MATLAB PROGRAMS% sorted is f(idx)[sorted idx] = sort(f);clear D sorted Xf(idx)=((1:M).^2)/M^2;% Create ordinal data matrixO = zeros(N,N);count = 1;for j=2:Nfor i=1:j-1O(i,j) = f(count);O(j,i) = f(count);count = count+1;endendclear f idxVn = sparse([-ones(1,N-1); eye(N-1)]);VOV = (-Vn’*O*Vn)/2;clear O Vnpack[evec evals flag] = eigs(VOV, speye(size(VOV)), 10, ’LR’);if flag, disp(’convergence problem’), return, end;evals = real(diag(evals));Xs = [zeros(3,1) diag(sqrt(evals(1:3)))*evec(:,1:3)’];warning off; Xsplot=zeros(3,lengthNaN)*(0/0); warning on;Xsplot(:,id) = Xs;figure(2)% plot map found via Ordinal MDS.plot3(Xsplot(1,:), Xsplot(2,:), Xsplot(3,:))axis equal, axis off
F.4. RANK REDUCTION SUBROUTINE, RRF() 659F.4 Rank reduction subroutine, RRf()(4.3.1.0.1)% Rank Reduction function -Jon Dattorro% Inputs are:% Xstar matrix,% affine equality constraint matrix A whose rows are in svec format.%% Tolerance scheme needs revision...function X = RRf(Xstar,A);rand(’seed’,23);m = size(A,1);n = size(Xstar,1);if size(Xstar,1)~=size(Xstar,2)disp(’Rank Reduction subroutine: Xstar not square’), pauseendtoler = norm(eig(Xstar))*size(Xstar,1)*1e-9;if sum(chop(eig(Xstar),toler)
- Page 608 and 609: 608 APPENDIX E. PROJECTIONThe test
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- Page 672 and 673: 672 APPENDIX G. NOTATION AND A FEW
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- Page 688 and 689: 688 BIBLIOGRAPHY[7] Abdo Y. Alfakih
- Page 690 and 691: 690 BIBLIOGRAPHY[27] Aharon Ben-Tal
- Page 692 and 693: 692 BIBLIOGRAPHY[48] Lev M. Brègma
- Page 694 and 695: 694 BIBLIOGRAPHY[67] Joel Dawson, S
- Page 696 and 697: 696 BIBLIOGRAPHY[85] Alan Edelman,
- Page 698 and 699: 698 BIBLIOGRAPHY[102] Philip E. Gil
- Page 700 and 701: 700 BIBLIOGRAPHYWeiss, editors, Pol
- Page 702 and 703: 702 BIBLIOGRAPHY[146] Jean-Baptiste
- Page 704 and 705: 704 BIBLIOGRAPHY[168] Jean B. Lasse
- Page 706 and 707: 706 BIBLIOGRAPHY[189] Rudolf Mathar
F.4. RANK REDUCTION SUBROUTINE, RRF() 659F.4 Rank reduction subroutine, RRf()(4.3.1.0.1)% Rank Reduction function -Jon Dattorro% Inputs are:% Xstar matrix,% affine equality constraint matrix A whose rows are in svec format.%% Tolerance scheme needs revision...function X = RRf(Xstar,A);rand(’seed’,23);m = size(A,1);n = size(Xstar,1);if size(Xstar,1)~=size(Xstar,2)disp(’Rank Reduction subroutine: Xstar not square’), pauseendtoler = norm(eig(Xstar))*size(Xstar,1)*1e-9;if sum(chop(eig(Xstar),toler)
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