# Objective: convex quadratic
# Constraints: linear

param m;
param n;

param b {1..m};
param A {1..m, 1..n};

var x {1..n} >= 0;
var t {1..m};

minimize sum_sqs: sum {i in 1..m} t[i]^2;

subject to defs {i in 1..m}: t[i] = b[i] - sum {j in 1..n} A[i,j]*x[j];

data;

param m := 500;
param n :=  150;
#param m := 1000;
#param n :=  300;
#param m := 512;
#param n := 1024;
let {i in 1..m, j in 1..n} A[i,j] := 0;
let {i in 1..m, j in 1..n: Uniform01() < 0.01} A[i,j] := Uniform01();
param x0 {j in 1..n} := Uniform01();
let {i in 1..m} b[i] := sum {j in 1..n} A[i,j]*x0[j] + Uniform01()-0.5;

#option loqo_options "timing=1 verbose=2";
#option minos_options "timing=1 superbasics=1000";
#option lancelot_options "timing=1";

#option solver loqo;		# 1m40.85s
#option solver minos;		# fails
#option solver lancelot;	# 1m12.86s

solve;