Initial Commit

CVXOPT Scripts/cvxOptTiming.py

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+from cvxopt import *
+from l1regls import *
+
+#Gen some random data
+m, n = 100, 1000
+A = normal(m, n)
+b = normal(m, 1)
+lam = 1
+
+###
+#Convert problem to standard form
+###
+P = spdiag( [2 * A.T * A] + [0] * n)
+
+ones = matrix([1.] * n)
+c = matrix([-2 * A.T * b, lam * ones])
+
+eye_n = spdiag([1.0] * n)
+G = matrix([ [eye_n, -1 * eye_n], [-1 * eye_n, -1 * eye_n] ])
+
+h = matrix(0., (2*n, 1) )
+
+def run():
+    for i in range(10):
+        sol=solvers.qp(P, c, G, h)
+#        l1regls(A, b)
+
+run()
+
+
+

CVXOPT Scripts/cvxOptTiming_specialized.py

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+import cvxopt
+import l1regls as l1
+
+def run():
+    for i in range(100):
+        l1.l1regls(A, b)
+
+m, n = 300, 30
+A = cvxopt.normal(300, 30)
+b = cvxopt.normal(300, 1)
+
+run()
+
+
+

CVXOPT Scripts/cvxopt_template.py

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+from cvxopt import *
+
+#Gen some random data
+m, n = 100, 1000
+A = normal(m, n)
+b = normal(m, 1)
+lam = 1
+
+###
+#Convert problem to standard form
+###
+
+
+
+
+
+#####
+def run():
+    for i in range(10):
+        sol=solvers.qp(P, c, G, h)
+
+run()
+
+
+

CVXOPT Scripts/cvxpy_timing.py

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+from cvxpy import *
+import numpy
+
+#gen some data
+m, n = 100, 20
+A, y = randn(m, n), randn(m, 1)
+
+#Build the lasso program
+#Note the similarity to a CVX style program
+lam = parameter(attribute='nonnegative')
+x = variable(n, 1, name="x")
+obj = minimize( norm2( y - A * x) + norm1(x))
+cnsts = []
+p = program(obj, cnsts)   
+p.solve()
+
+####
+# Timing test.  
+# Only run once... bc it's dense
+for i in range(10):
+    lam.value = 1
+    p.solve()
+
+

CVX_Scripts/LoopedLeastSquares.m

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+%%%%%%%
+% Regularized Least Squares in 'For' Loop
+%%%%%%%
+% Created by V. Gupta 13 Jan 2013
+
+
+%% Load test data from a file
+y = csvread('testResponse.csv');
+A = csvread('testSignals.csv');
+m = size(A, 1);
+n = size(A, 2);
+
+%% Loop version of Least Squares
+cvx_begin
+    variable x(n) 
+    variable r(m)
+
+    for i = 1:m
+        r(i) == y(i) - A(i, :) * x
+    end
+
+    minimize norm(r, 2) + norm(x, 1)
+cvx_end
+
+%Question:  how do we incorporate dual variables

CVX_Scripts/LoopedLeastSquares_dual.m

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+%%%%%%%
+% Regularized Least Squares in 'For' Loop
+%%%%%%%
+% Created by V. Gupta 13 Jan 2013
+
+
+%% Load test data from a file
+y = csvread('testResponse.csv');
+A = csvread('testSignals.csv');
+m = size(A, 1);
+n = size(A, 2);
+
+%% Loop version of Least Squares
+cvx_begin
+    variables x(n) r(m)
+    dual variable p{m}
+
+    for i = 1:m
+        p{i} : r(i) == y(i) - A(i, :) * x
+    end
+
+    minimize norm(r, 2) + norm(x, 1)
+cvx_end

CVX_Scripts/MomentProblems.m

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+%%%%%%%
+% Moment Problems
+% Finds a max entropy distribution on given support
+% that approximately satisfies the given moment conditions
+%%%%%%%
+% Created by V. Gupta 13 Jan 2013
+
+%% Read in the required moments
+moments = csvread('Moments.csv');
+numMoments = size(moments, 1);
+
+%% Form required optimization problem
+supp = (1:100)./10;
+cvx_begin
+    variable p(length(supp))
+    maximize sum(entr(p));
+
+    %must be a probability
+    p >= 0;
+    sum(p) == 1;  
+
+    for i = 1:numMoments
+        supp.^i * p <= 1.05 * moments(i);
+        supp.^i * p >= .95 * moments(i);
+    end
+
+cvx_end
+
+%% Plot some output
+figure(1)
+bar(p)
+ylabel('Prob', 'FontSize', 15)
+title('Distribution', 'FontSize', 15)
+
+%Plot the dual variables
+figure(2)
+
+
+%% Tasks:
+% Add dual variable for the normalization constraint
+% Add dual variables for the moment constraints
+% Add a plot for of the dual variables in figure(2)
+
+%% Challenge questions:
+% Could you have written this optimization without the loop?

CVX_Scripts/Moments.csv

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+5.9484
+38.877
+271.62
+1997.6
+15303
+1.2119e+05
+9.8648e+05
+8.2157e+06

CVX_Scripts/SimpleSDP.m

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+%%% Simple example demonstrating SDP functionality for CVX
+% Created by V. Gupta 24 Jan 2013
+cvx_begin
+    variable X(3, 3)
+    X == semidefinite(3)
+
+    5 * X(1,1) + 2 * X(2, 3) - X(3, 3) == 1
+    2 * X(2, 2) + 3 * X(3, 3) <= 2
+
+    minimize 3 * X(1, 1) - 2 * X(2, 3)
+
+
+cvx_end

CVX_Scripts/Simpledual.m

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+%%%%%%%
+% Max Entropy Problem with Dual Vars
+% Solves a simple max-entropy problem on given
+% support
+%%%%%%%
+% Created by V. Gupta 1 Jan 2013
+
+supp = 1:10;
+
+cvx_begin
+    variable p(length(supp))
+    maximize sum(entr(p))
+
+    %must be a probability
+    sum(p) == 1;  p >= 0;
+
+    %Constrain mean
+    %But incorporate a dual variable
+    %notice we DO NOT write dual variable lambda(1)
+    dual variable lambda
+    lambda : supp * p == 4;
+
+cvx_end
+
+%Plot some output
+p
+bar(p)
+ylabel('Prob', 'FontSize', 15)
+title('Max Entropy Distribution', 'FontSize', 15)

CVX_Scripts/cvxTimingComparisons.m

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+%%%%%%%
+% Timing Comparisons for CVX on regularized least squares
+%%%%%%%
+% Created by V. Gupta 13 Jan 2013
+
+
+%Gen some random data
+m = 100;
+n = 20;
+A = randn(m, n);
+y = randn(m, 1);
+lambda = 2.^(.1 * (0:99) - 5)
+tot_cputime = 0;
+tot_time = 0;
+tic;
+for i = 10:10:100
+    cvx_begin 
+        variable x(n) 
+        minimize norm(y - A*x, 2) + lambda(i) * norm(x, 1)
+
+    %uncomment this tic to geta n approx solver time
+    %tic;    
+    cvx_end
+    tot_time = tot_time + toc;
+
+    tot_cputime = tot_cputime + cvx_cputime;
+end
+
+tot_cputime
+tot_time
+tot_time / tot_cputime
+
+% Gurobi
+% 53.2 s cputime
+% 22.9 s tot_time
+