P = [13 12 -2; 12 17 6; -2 6 12];
q = [-22; -14.5; 13];
r = 1;
n = 3;
x_star = [1;1/2;-1];
fprintf(1,'Computing the optimal solution ...');
cvx_begin
variable x(n)
minimize ( (1/2)*quad_form(x,P) + q'*x + r)
x >= -1;
x <= 1;
cvx_end
fprintf(1,'Done! \n');
disp('------------------------------------------------------------------------');
disp('The computed optimal solution is: ');
disp(x);
disp('The given optimal solution is: ');
disp(x_star);
Computing the optimal solution ...
Calling Mosek 9.1.9: 11 variables, 4 equality constraints
For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4
Cones : 1
Scalar variables : 11
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4
Cones : 1
Scalar variables : 11
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 4
Optimizer - Cones : 1
Optimizer - Scalar variables : 11 conic : 5
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 10 after factor : 10
Factor - dense dim. : 0 flops : 8.80e+01
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.2e+01 2.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.00
1 5.2e+00 4.7e-01 4.3e-01 -9.18e-01 1.938016332e+01 2.180410014e+01 2.4e-01 0.01
2 2.7e+00 2.4e-01 1.4e-01 5.16e-02 2.492288513e+01 2.574944173e+01 1.2e-01 0.01
3 5.2e-01 4.7e-02 1.5e-02 3.72e-01 3.668100946e+01 3.697652591e+01 2.4e-02 0.01
4 1.7e-01 1.5e-02 2.9e-03 9.10e-01 3.822094097e+01 3.832464600e+01 7.7e-03 0.01
5 2.9e-02 2.7e-03 2.1e-04 9.72e-01 3.895264887e+01 3.897124371e+01 1.3e-03 0.01
6 5.9e-03 5.4e-04 1.9e-05 9.94e-01 3.908479462e+01 3.908876214e+01 2.7e-04 0.01
7 9.4e-05 8.5e-06 4.0e-08 9.98e-01 3.912442958e+01 3.912449642e+01 4.3e-06 0.01
8 1.2e-06 1.1e-07 5.6e-11 1.00e+00 3.912499409e+01 3.912499493e+01 5.4e-08 0.01
9 1.2e-07 1.1e-08 1.9e-12 1.00e+00 3.912499944e+01 3.912499953e+01 5.5e-09 0.01
10 5.9e-09 5.4e-10 2.2e-14 1.00e+00 3.912499997e+01 3.912499998e+01 2.7e-10 0.01
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.9124999974e+01 nrm: 3e+01 Viol. con: 3e-08 var: 0e+00 cones: 0e+00
Dual. obj: 3.9124999978e+01 nrm: 2e+00 Viol. con: 0e+00 var: 3e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 10 time: 0.01
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -21.625
Done!
------------------------------------------------------------------------
The computed optimal solution is:
1.0000
0.5000
-1.0000
The given optimal solution is:
1.0000
0.5000
-1.0000