function?[z?history]?=?quadprog（P?q?r?lb?ub?rho?alpha）
%?quadprog??Solve?standard?form?box-constrained?QP?via?ADMM
%
%?[x?history]?=?quadprog（P?q?r?lb?ub?rho?alpha）
%
%?Solves?the?following?problem?via?ADMM:
%
%???minimize?????（1/2）*x‘*P*x?+?q‘*x?+?r
%???subject?to???lb?<=?x?<=?ub
%
%?The?solution?is?returned?in?the?vector?x.
%
%?history?is?a?structure?that?contains?the?objective?value?the?primal?and
%?dual?residual?norms?and?the?tolerances?for?the?primal?and?dual?residual
%?norms?at?each?iteration.
%
%?rho?is?the?augmented?Lagrangian?parameter.
%
%?alpha?is?the?over-relaxation?parameter?（typical?values?for?alpha?are
%?between?1.0?and?1.8）.
%
%
%?More?information?can?be?found?in?the?paper?linked?at:
%?http://www.stanford.edu/~boyd/papers/distr_opt_stat_learning_admm.html
%

t_start?=?tic;
%%?Global?constants?and?defaults

QUIET????=?0;
MAX_ITER?=?1000;
ABSTOL???=?1e-4;
RELTOL???=?1e-2;
%%?Data?preprocessing

n?=?size（P1）;
%%?ADMM?solver

x?=?zeros（n1）;
z?=?zeros（n1）;
u?=?zeros（n1）;

if?~QUIET
????fprintf（‘%3s\t%10s\t%10s\t%10s\t%10s\t%10s\n‘?‘iter‘?...
??????‘r?norm‘?‘eps?pri‘?‘s?norm‘?‘eps?dual‘?‘objective‘）;
end

for?k?=?1:MAX_ITER

????if?k?>?1
????????x?=?R?\?（R‘?\?（rho*（z?-?u）?-?q））;
????else
????????R?=?chol（P?+?rho*eye（n））;???%%?分解為一個上三角矩陣
????????x?=?R?\?（R‘?\?（rho*（z?-?u）?-?q））;
????end

????%?z-update?with?relaxation
????zold?=?z;
????x_hat?=?alpha*x?+（1-alpha）*zold;
????z?=?min（ub?max（lb?x_hat?+?u））;

????%?u-update
????u?=?u?+?（x_hat?-?z）;

????%?diagnostics?reporting?termination?checks
????history.objval（k）??=?objective（P?q?r?x）;

????history.r_norm（k）??=?norm（x?-?z）;
????history.s_norm（k）??=?norm（-rho*（z?-?zold））;

????history.eps_pri（k）?=?sqrt（n）*ABSTOL?+?RELTOL*max（norm（x）?norm（-z））;
????history.eps_dual（k）=?sqrt（n）*ABSTOL?+?RELTOL*norm（rho*u）;

????if?~QUIET
????????fprintf（‘%3d\t%10.4f\t%10.4f\t%10.4f\t%10.4f\t%10.2f\n‘?k?...
????????????history.r_norm（k）?history.eps_pri（k）?...
????????????history.s_norm（k）?history.eps_dual（k）?history.objval（k））;
????end

????if?（history.r_norm（k）????????history.s_norm（k）??????????break;
????end
end

if?~QUIET
????toc（t_start）;
end
end

function?obj?=?objective（P?q?r?x）
????obj?=?0.5*x‘*P*x?+?q‘*x?+?r;
end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????2395??2016-08-11?11:40??ADMM_quadprog\quadprog.m

?????文件????????930??2016-09-26?21:54??ADMM_quadprog\quadprog_main.m

?????目錄??????????0??2016-09-26?21:55??ADMM_quadprog

-----------?---------??----------?-----??----

?????????????????3325????????????????????3