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t_mips.m
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t_mips.m
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function t_mips(quiet)
% t_mips - Tests of mips, MIPS NLP solver.
% ::
%
% t_mips
% t_mips(quiet)
% MIPS
% Copyright (c) 2010-2024, Power Systems Engineering Research Center (PSERC)
% by Ray Zimmerman, PSERC Cornell
%
% This file is part of MIPS.
% Covered by the 3-clause BSD License (see LICENSE file for details).
% See https://github.com/MATPOWER/mips for more info.
if nargin < 1
quiet = 0;
end
num_tests = 60;
t_begin(num_tests, quiet);
t = 'unconstrained banana function : ';
%% from MATLAB Optimization Toolbox's bandem.m
f_fcn = @(x)f2(x);
x0 = [-1.9; 2];
% [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], [], [], [], [], struct('verbose', 2));
[x, f, s, out, lam] = mips(f_fcn, x0);
t_is(s, 1, 13, [t 'success']);
t_is(x, [1; 1], 13, [t 'x']);
t_is(f, 0, 13, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = 'unconstrained 3-d quadratic : ';
%% from http://www.akiti.ca/QuadProgEx0Constr.html
f_fcn = @(x)f3(x);
x0 = [0; 0; 0];
% [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], [], [], [], [], struct('verbose', 2));
[x, f, s, out, lam] = mips(f_fcn, x0);
t_is(s, 1, 13, [t 'success']);
t_is(x, [3; 5; 7], 13, [t 'x']);
t_is(f, -244, 13, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = 'constrained 4-d QP : ';
%% from https://v8doc.sas.com/sashtml/iml/chap8/sect12.htm
f_fcn = @(x)f4(x);
x0 = [1; 0; 0; 1];
A = [ 1 1 1 1;
0.17 0.11 0.10 0.18 ];
l = [1; 0.10];
u = [1; Inf];
xmin = zeros(4,1);
% [x, f, s, out, lam] = mips(f_fcn, x0, A, l, u, xmin, [], [], [], struct('verbose', 2));
[x, f, s, out, lam] = mips(f_fcn, x0, A, l, u, xmin);
t_is(s, 1, 13, [t 'success']);
t_is(x, [0; 2.8; 0.2; 0]/3, 6, [t 'x']);
t_is(f, 3.29/3, 6, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
% %% check with quadprog (for dev testing only)
% H = [ 1003.1 4.3 6.3 5.9;
% 4.3 2.2 2.1 3.9;
% 6.3 2.1 3.5 4.8;
% 5.9 3.9 4.8 10 ];
% c = zeros(4,1);
% [x, f, s, out, lam] = quadprog(H,c,-A(2,:), -0.10, A(1,:), 1, xmin);
% t_is(s, 1, 13, [t 'success']);
% t_is(x, [0; 2.8; 0.2; 0]/3, 6, [t 'x']);
% t_is(f, 3.29/3, 6, [t 'f']);
% t_is(lam.eqlin, -6.58/3, 6, [t 'lam.eqlin']);
% t_is(lam.ineqlin, 0, 13, [t 'lam.ineqlin']);
% t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
% t_is(lam.upper, [0;0;0;0], 13, [t 'lam.upper']);
t = 'constrained 2-d nonlinear : ';
%% from https://en.wikipedia.org/wiki/Nonlinear_programming#2-dimensional_example
f_fcn = @(x)f5(x);
gh_fcn = @(x)gh5(x);
hess_fcn = @(x, lam, cost_mult)hess5(x, lam, cost_mult);
x0 = [1.1; 0];
xmin = zeros(2, 1);
% xmax = 3 * ones(2, 1);
% [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, [], gh_fcn, hess_fcn, struct('verbose', 2));
[x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, [], gh_fcn, hess_fcn);
t_is(s, 1, 13, [t 'success']);
t_is(x, [1; 1], 6, [t 'x']);
t_is(f, -2, 6, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_is(lam.ineqnonlin, [0;0.5], 6, [t 'lam.ineqnonlin']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
% %% check with fmincon (for dev testing only)
% % fmoptions = optimset('Algorithm', 'interior-point');
% % [x, f, s, out, lam] = fmincon(f_fcn, x0, [], [], [], [], xmin, [], gh_fcn, fmoptions);
% [x, f, s, out, lam] = fmincon(f_fcn, x0, [], [], [], [], [], [], gh_fcn);
% t_is(s, 1, 13, [t 'success']);
% t_is(x, [1; 1], 4, [t 'x']);
% t_is(f, -2, 6, [t 'f']);
% t_is(lam.ineqnonlin, [0;0.5], 6, [t 'lam.ineqnonlin']);
t = 'constrained 3-d nonlinear : ';
%% from https://en.wikipedia.org/wiki/Nonlinear_programming#3-dimensional_example
f_fcn = @(x)f6(x);
gh_fcn = @(x)gh6(x);
hess_fcn = @(x, lam, cost_mult)hess6(x, lam, cost_mult);
x0 = [1; 1; 0];
% [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], [], [], gh_fcn, hess_fcn, struct('verbose', 2, 'comptol', 1e-9));
[x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], [], [], gh_fcn, hess_fcn);
t_is(s, 1, 13, [t 'success']);
t_is(x, [1.58113883; 2.23606798; 1.58113883], 6, [t 'x']);
t_is(f, -5*sqrt(2), 6, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_is(lam.ineqnonlin, [0;sqrt(2)/2], 7, [t 'lam.ineqnonlin']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
% %% check with fmincon (for dev testing only)
% % fmoptions = optimset('Algorithm', 'interior-point');
% % [x, f, s, out, lam] = fmincon(f_fcn, x0, [], [], [], [], xmin, [], gh_fcn, fmoptions);
% [x, f, s, out, lam] = fmincon(f_fcn, x0, [], [], [], [], [], [], gh_fcn);
% t_is(s, 1, 13, [t 'success']);
% t_is(x, [1.58113883; 2.23606798; 1.58113883], 4, [t 'x']);
% t_is(f, -5*sqrt(2), 8, [t 'f']);
% t_is(lam.ineqnonlin, [0;sqrt(2)/2], 8, [t 'lam.ineqnonlin']);
t = 'constrained 3-d nonlinear (struct) : ';
p = struct('f_fcn', f_fcn, 'x0', x0, 'gh_fcn', gh_fcn, 'hess_fcn', hess_fcn);
[x, f, s, out, lam] = mips(p);
t_is(s, 1, 13, [t 'success']);
t_is(x, [1.58113883; 2.23606798; 1.58113883], 6, [t 'x']);
t_is(f, -5*sqrt(2), 6, [t 'f']);
t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
t_is(lam.ineqnonlin, [0;sqrt(2)/2], 7, [t 'lam.ineqnonlin']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = 'constrained 4-d nonlinear : ';
%% Hock & Schittkowski test problem #71
f_fcn = @(x)f7(x);
gh_fcn = @(x)gh7(x);
hess_fcn = @(x, lam, sigma)hess7(x, lam, sigma);
x0 = [1; 5; 5; 1];
xmin = ones(4, 1);
xmax = 5 * xmin;
% [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, xmax, gh_fcn, hess_fcn, struct('verbose', 2, 'comptol', 1e-9));
[x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, xmax, gh_fcn, hess_fcn);
t_is(s, 1, 13, [t 'success']);
t_is(x, [1; 4.7429994; 3.8211503; 1.3794082], 6, [t 'x']);
t_is(f, 17.0140173, 6, [t 'f']);
t_is(lam.eqnonlin, 0.1614686, 5, [t 'lam.eqnonlin']);
t_is(lam.ineqnonlin, 0.55229366, 5, [t 'lam.ineqnonlin']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, [1.08787121024; 0; 0; 0], 5, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 7, [t 'lam.upper']);
t_end;
% %%----- eg99 : linearly constrained fmincon example, mips can't solve -----
% function [f, df, d2f] = eg99(x)
% f = -x(1)*x(2)*x(3);
% df = -[ x(2)*x(3);
% x(1)*x(3);
% x(1)*x(2) ];
% d2f = -[ 0 x(3) x(2);
% x(3) 0 x(1);
% x(2) x(1) 0 ];
% end
%
% x0 = [10;10;10];
% A = [1 2 2];
% l = 0;
% u = 72;
% fmoptions = optimset('Display', 'testing');
% fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point');
% [x, f, s, out, lam] = fmincon(f_fcn, x0, [-A; A], [-l; u], [], [], [], [], [], fmoptions);
% t_is(x, [24; 12; 12], 13, t);
% t_is(f, -3456, 13, t);
%% unconstrained banana function
%% from MATLAB Optimization Toolbox's bandem.m
function [f, df, d2f] = f2(x)
a = 100;
f = a*(x(2)-x(1)^2)^2+(1-x(1))^2;
df = [ 4*a*(x(1)^3 - x(1)*x(2)) + 2*x(1)-2;
2*a*(x(2) - x(1)^2) ];
d2f = 4*a*[ 3*x(1)^2 - x(2) + 1/(2*a), -x(1);
-x(1) 1/2 ];
%% unconstrained 3-d quadratic
%% from http://www.akiti.ca/QuadProgEx0Constr.html
function [f, df, d2f] = f3(x)
H = [5 -2 -1; -2 4 3; -1 3 5];
c = [2; -35; -47];
f = 1/2 * x'*H*x + c'*x + 5;
df = H*x + c;
d2f = H;
%% constrained 4-d QP
%% from https://v8doc.sas.com/sashtml/iml/chap8/sect12.htm
function [f, df, d2f] = f4(x)
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ];
c = zeros(4,1);
f = 1/2 * x'*H*x + c'*x;
df = H*x + c;
d2f = H;
%% constrained 2-d nonlinear
%% from https://en.wikipedia.org/wiki/Nonlinear_programming#2-dimensional_example
function [f, df, d2f] = f5(x)
c = -[1; 1];
f = c'*x;
df = c;
d2f = zeros(2,2);
function [h, g, dh, dg] = gh5(x)
h = [ -1 -1; 1 1] * x.^2 + [1; -2];
dh = 2 * [-x(1) x(1); -x(2) x(2)];
g = []; dg = [];
function Lxx = hess5(x, lam, cost_mult)
mu = lam.ineqnonlin;
Lxx = 2*[-1 1]*mu*eye(2);
%% constrained 3-d nonlinear
%% from https://en.wikipedia.org/wiki/Nonlinear_programming#3-dimensional_example
function [f, df, d2f] = f6(x)
f = -x(1)*x(2) - x(2)*x(3);
df = -[x(2); x(1)+x(3); x(2)];
d2f = -[0 1 0; 1 0 1; 0 1 0];
function [h, g, dh, dg] = gh6(x)
h = [ 1 -1 1; 1 1 1] * x.^2 + [-2; -10];
dh = 2 * [x(1) x(1); -x(2) x(2); x(3) x(3)];
g = []; dg = [];
function Lxx = hess6(x, lam, cost_mult)
if nargin < 3, cost_mult = 1; end
mu = lam.ineqnonlin;
Lxx = cost_mult * [0 -1 0; -1 0 -1; 0 -1 0] + ...
[2*[1 1]*mu 0 0; 0 2*[-1 1]*mu 0; 0 0 2*[1 1]*mu];
%% constrained 4-d nonlinear
%% Hock & Schittkowski test problem #71
function [f, df, d2f] = f7(x)
f = x(1)*x(4)*sum(x(1:3)) + x(3);
df = [ x(1)*x(4) + x(4)*sum(x(1:3));
x(1)*x(4);
x(1)*x(4) + 1;
x(1)*sum(x(1:3)) ];
d2f = sparse([ 2*x(4) x(4) x(4) 2*x(1)+x(2)+x(3);
x(4) 0 0 x(1);
x(4) 0 0 x(1);
2*x(1)+x(2)+x(3) x(1) x(1) 0
]);
function [h, g, dh, dg] = gh7(x)
g = sum(x.^2) - 40;
h = -prod(x) + 25;
dg = 2*x;
dh = -prod(x)./x;
function Lxx = hess7(x, lam, sigma)
if nargin < 3, sigma = 1; end
lambda = lam.eqnonlin;
mu = lam.ineqnonlin;
[f, df, d2f] = f7(x);
Lxx = sigma * d2f + lambda*2*speye(4) - ...
mu*sparse([ 0 x(3)*x(4) x(2)*x(4) x(2)*x(3);
x(3)*x(4) 0 x(1)*x(4) x(1)*x(3);
x(2)*x(4) x(1)*x(4) 0 x(1)*x(2);
x(2)*x(3) x(1)*x(3) x(1)*x(2) 0 ]);