Please note that the recommended version of Scilab is 2023.1.0. This page might be outdated.
See the recommended documentation of this function
m x 1 real column vector (must be strictly primal feasible, see below)
L x 1 real vector (compressed form of a strictly feasible dual matrix, see below)
L x (m+1) real matrix
p x 2 integer matrix (sizes of the blocks) defining the dimensions of the (square) diagonal blocks
m x 1 real vector
row vector with five entries
row vector with two entries
solves semidefinite program:
and its dual:
exploiting block structure in the matrices
It interfaces L. Vandenberghe and S. Boyd sp.c program.
Fi's matrices are stored columnwise in
F in compressed format: if
i=0,..,m, j=1,...,L denote the jth (symmetric) diagonal block of
pack(M), for symmetric
M, is the vector
(obtained by scanning columnwise the lower triangular part of
blck_szs gives the size of block
Z is a block diagonal matrix with L blocks
Z^j has size
times blck_szs[j]. Every block is stored using packed storage of
the lower triangular part.
The 2 vector
ul contains the primal objective
c'*x and the dual objective value
The entries of
options are respectively:
nu = a real parameter which ntrols the rate of
abstol = absolute tolerance.
reltol = relative tolerance (has a special meaning when
tv target value, only referenced if
reltol < 0.
iters = on entry:
maximum number of iterations >= 0, on exit: the number of iterations
taken. Notice that the absolute tolerance cannot be lower than 1.0e-8,
that is, the absolute tolerance used in the algorithm is the maximum of
the user-defined tolerance and the constant tolerance 1.0e-8.
info returns 1 if maxiters exceeded, 2 if
absolute accuracy is reached, 3 if relative accuracy is reached, 4 if
target value is reached, 5 if target value is not achievable; negative
values indicate errors.
(1) maxiters is exceeded (2) duality gap is less than abstol (3) primal and dual objective are both positive and duality gap is less than (reltol * dual objective) or primal and dual objective are both negative and duality gap is less than (reltol * minus the primal objective) (4) reltol is negative and primal objective is less than tv or dual objective is greater than tv
F0=[2,1,0,0; 1,2,0,0; 0,0,3,1 0,0,1,3]; F1=[1,2,0,0; 2,1,0,0; 0,0,1,3; 0,0,3,1] F2=[2,2,0,0; 2,2,0,0; 0,0,3,4; 0,0,4,4]; blck_szs=[2,2]; F01=F0(1:2,1:2);F02=F0(3:4,3:4); F11=F1(1:2,1:2);F12=F1(3:4,3:4); F21=F2(1:2,1:2);F22=F2(3:4,3:4); x0=[0;0] Z0=2*F0; Z01=Z0(1:2,1:2);Z02=Z0(3:4,3:4); FF=[[F01(:);F02(:)],[F11(:);F12(:)],[F21(:);F22(:)]] ZZ0=[[Z01(:);Z02(:)]]; c=[trace(F1*Z0);trace(F2*Z0)]; options=[10,1.d-10,1.d-10,0,50]; [x,Z,ul,info]=semidef(x0,pack(ZZ0),pack(FF),blck_szs,c,options) w=vec2list(unpack(Z,blck_szs),[blck_szs;blck_szs]);Z=sysdiag(w(1),w(2)) c'*x+trace(F0*Z) spec(F0+F1*x(1)+F2*x(2)) trace(F1*Z)-c(1) trace(F2*Z)-c(2)
L. Vandenberghe and S. Boyd, " Semidefinite Programming," Informations Systems Laboratory, Stanford University, 1994.
Ju. E. Nesterov and M. J. Todd, "Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming," Working Paper, CORE, Catholic University of Louvain, Louvain-la-Neuve, Belgium, April 1994.
SP: Software for Semidefinite Programming, http://www.ee.ucla.edu/~vandenbe/sp.html
|<< recons||Otimização e Simulação||vec2list >>|