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accelerated prox-level and uniform smoothing level methods for solvin…
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…g the maximum eigenvalue problem
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@linboqiao
linboqiao committed Mar 26, 2017
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10 changes: 10 additions & 0 deletions AC-SA/Results.txt
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*** Running Single-stage AC-SA

Runtime: 0.26 Final objective value: 10.41

********** Data: N100-d30-st3.mat , rho: 0.1

*** Running Batch-learning

Runtime: 0.00 Final objective value: 10.51

*** Running Classic SA

Runtime: 0.26 Final objective value: 11697.10
214 changes: 214 additions & 0 deletions APL/APL-Eigen/APL_Eigen_basic.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATLAB Code for the Accelerated Prox-Level (APL) algorithm %
% Author: Guanghui (George) Lan %
% Institute: University of Florida, Industrial & Systems Engineering %
% @All rights reserved 2010 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% this file implements an APL algorithm for solving QP %
function APL_Eigen_basic(control, domain, data)

% compute the initial lower and upper bound
data.mu = 0;

if data.DomainType == 0, %simplex
p0 = ones(domain.n,1)/domain.n;
[f,g,f0] = oracle(data, p0, 0);
UB = f0; % initial upper bound
% compute the initial lower bound
% min f0(p_0) + <f0'(p_0), x - p_0>: x in X
% X is a standard simplex < Bnd
Bnd = 1;

[v,I] = min(g);
t_p0 = zeros(domain.n,1);
t_p0(I) = Bnd;

LB = f0 + g' * (t_p0 - p0); % initial lower bound
else
if data.DomainType == 1 %box [0,1] domain, and using \|.\|^2/2 prox-function
p0 = zeros(domain.n,1);
[f,g,f0] = oracle(data, p0, 0);
UB = f0;
% min f0(p_0) + <f0'(p_0), x - p_0>: x in X, X is box
LB = f0 - g'*p0 + sum(min(0,g));
else %box [0,1] domain, but we embed it into a 1 \le \sum x_i \le n using
% the prox-function \sum_i x/n log x/n
p0 = ones(domain.n,1);
[f,g,f0] = oracle(data, p0, 0);
UB = f0;
% min f0(p_0) + <f0'(p_0), x - p_0>: x in X, X is box
LB = f0 - g'*p0 + sum(min(0,g));
end
end

% select the initial prox center
prox_center = p0;
x_ubt = p0;

nstep = 0;
s = 0;

start_APL=clock;
% define the bundle structure
Bundle.size = 0;
Bundle.matrix = zeros(control.bundle_limit, domain.n);
Bundle.const = zeros(control.bundle_limit, 1);
lb_dual = 0;
map_dual = 0;

basemu = control.theta * (1-control.lambda) / (2*log(data.m));

terminate = 0;
while terminate == 0
if (UB - LB <= control.epsilon || nstep > control.iter_limit )
break;
end

% start stage s = 1, 2,..
s = s+1;
xt = x_ubt;
c = x_ubt;
LS = LB + control.lambda * (UB - LB);
stepLB = LB;
stepUB = UB;

% update the smoothing parameter
data.mu = basemu * (UB-LB);

% if data.mu < control.epsilon
% data.mu = control.epsilon;
% end

% data.mu = 0;
% clear up the constraint that defines \bar(X)
BarX.a = zeros(domain.n, 1);
BarX.b = 0;

t = 0;

while 1 == 1
nstep = nstep + 1;
t = t + 1;
alpha_t = 2.0 / (t + 1.0);

if (stepUB - stepLB <= control.epsilon || nstep > control.iter_limit )
terminate = 1;
break;
end

% obtain an initial feasible solution to X_t for the computation of
% the lower bound

x_lbt = (1 - alpha_t) * x_ubt + alpha_t * xt;
[f,g,f0,dlb]= oracle(data, x_lbt, 0);

disp(sprintf('nstep=%d, UB=%.6e, LB=%.6e, stepUB=%.6e, stepLB=%.6e, Gap=%.6e, Bundle=%d\n',...
nstep, UB, LB, stepUB, stepLB, stepUB-stepLB,Bundle.size));
if nstep > control.iter_limit
break;
end

if data.DomainType == 0,
hstar = ComputeNewLB(domain, Bundle, data, BarX, f, g, x_lbt, LS, control.lb_mode);
else,
hstar = ComputeNewLB_box(domain, Bundle, data, BarX, f, g, x_lbt, LS, control.lb_mode);
end;
% hstar = ComputeNewLBCVX(domain, Bundle, data, BarX, f, g, x_lbt, LS, control.lb_mode);

stepLB = max(stepLB, min(hstar,LS));

% if stepLB <dlb,
% stepLB = dlb;
% end


% if control.bundle_limit > 0,
% if Bundle.size < control.bundle_limit
% Bundle.size = Bundle.size + 1;
% Bundle.matrix(Bundle.size, :) = g';
% Bundle.const(Bundle.size) = f - g'* x_lbt;
% else
% Bundle.matrix(1:Bundle.size-1, :) = Bundle.matrix(2:Bundle.size, :);
% Bundle.const(1:Bundle.size-1) = Bundle.const(2:Bundle.size);
% Bundle.matrix(Bundle.size, :) = g';
% Bundle.const(Bundle.size) = f - g'* x_lbt;
% end
% end

if control.bundle_limit > 0,
if Bundle.size < control.bundle_limit
Bundle.size = Bundle.size + 1;
newguy = Bundle.size;
else % remove the oldest guy
newguy = mod(nstep-1, control.bundle_limit)+1;
end
Bundle.matrix(newguy, :) = g';
Bundle.const(newguy) = f - g'* x_lbt;
end

% significant progress on the lower bound
if stepLB >= LS - control.theta * (LS - LB),
LB = stepLB;
UB = stepUB;
c = x_ubt;
break;
else,
% xt = ProxMappingCVX(domain, Bundle, data, BarX, f, g, x_lbt, c, LS);
if data.DomainType == 0,
xt = ComputeProxMapping(domain, Bundle, data, BarX, f, g, x_lbt, c, LS);
else
if data.DomainType == 1,
xt = ComputeProxMapping_box(domain, Bundle, data, BarX, f, g, x_lbt, c, LS);
else
xt = ComputeProxMapping_box_entropy(domain, Bundle, data, BarX, f, g, x_lbt, c, LS);
end
end;

tmp_xub = alpha_t * xt + (1 - alpha_t) * x_ubt;
[fu, gu, f0u] = oracle(data, tmp_xub, 1);
if f0u < stepUB,
stepUB = f0u;
x_ubt = tmp_xub;
end

% the constraint that defines \bar{X}
% BarX.a = xt - c;
% the constraint that defines \bar{X}
% domega_c x_t (x - x_t) \ge 0
% note that domega x_t =
if data.DomainType == 0,
BarX.a = log(xt) - log(c);
else
if data.DomainType == 1,
BarX.a = xt - c;
else
BarX.a = (log(xt/domain.n) - log(c/domain.n)) / domain.n;
end
end;

BarX.b = BarX.a' * xt;


% significant progress on the upper bound
if stepUB <= LS + control.theta * (UB - LS),
LB = stepLB;
UB = stepUB;
c = x_ubt;
break;
end
end
end
end
time_APL=etime(clock,start_APL);
disp(sprintf('end of execution.\n'));
str = sprintf('nstep=%d, UB=%.6e, LB=%.6e, stepUB=%.6e, stepLB=%.6e, time=%5.2f\n',...
nstep, UB, LB, stepUB, stepLB, time_APL);
disp(str);
frep = fopen('report.txt','a');
fprintf(frep,'Summary: %s**\n',str);
fclose(frep);




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