MATLAB: Quadprog different output for R2020a and R2017a

bugquadprog

Hello,
If I run quadprog minimization function I get completely different results on R2020a and R2017a. It seems that the output on the lattest release is wrong. Did something changed? Is it a bug you are aware of?
Kind regards

Best Answer

There is an option called 'LinearSolver'. It can be dense or sparse. I set it to sparse and it converged quickly.
This problem is solvable but be careful with the condition number of the H matrix. i.e. cond(H). The higher the condition number, the more ill-conditioned the problem. ill-condition problems are harder to solve. With the generic cost: J = 1/2*x'*H*x+f'*x. Small pertubations to f will cause large changes to the solution, x. 
% Load files
structure = load('quadprog_input.mat');
H = structure.quadprog_input.H;         % 404x404 matrix
f = structure.quadprog_input.f;         % 1x404 vector
Aineq = structure.quadprog_input.Aineq; % 808x404 matrix
bineq = structure.quadprog_input.bineq; % 808x1 vector
% opt   = structure.quadprog_input.opt;
% with opt.TolCon = 100*eps, opt.TollFun = 100*eps, opt.Display = 'none',
% opt.Algorithm = 'interior-point-convex
Aeq = [];
beq = [];
f = f'; % f should be 404x1
% Objective is 1/2*dp'*2*H*dp+f'*dp
%                  
% dp' is 1x404
% dp is 404x1
% 2*H is 404x404
% f is 404x1
% f' is 1x404
%

%   1/2*dp' * 2*H   *dp   + f'   *dp
%      1x404 404x404 404x1  1x404 404x1
%      1x1                + 1x1
%      1x1
% Thus, f should be 404x1
%
opt = optimoptions('quadprog', 'TolCon', 100*eps, 'TolFun', 100*eps, ... 
     'Display', 'iter-detailed', 'Algorithm', 'interior-point-convex', ...
     'MaxIter', 1500,'LinearSolver','sparse');
% Best case cost ignoring constraints
[~,fval,~] = quadprog(2*H,f,[], [], [], [],[],[],[],opt)
% solve quadprog problem. Note this doesn't converge
[dp,fval,~] = quadprog(2*H,f,Aineq, bineq, Aeq, beq,[],[],[],opt); fval
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