# HELP: Status: Unbounded Optimal value (cvx_optval): +Inf

I have used the successive convex approximation to transform the problem into a convex optimization problem, but there is still something wrong when solving the problem by CVX with MOSEK. Message of CVX is as follows:

## Calling Mosek 9.1.9: 3900 variables, 1802 equality constraints

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1802
Cones : 800
Scalar variables : 3900
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 0 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Optimizer terminated. Time: 0.05

Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.0873703084e-08 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.05
Interior-point - iterations : 0 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: Unbounded
Optimal value (cvx_optval): +Inf

Is CVX unable to solve this problem? My code is as follows:

cvx_begin
cvx_solver mosek
variable traj(para.T+1, 2)
variable u(1, para.T)
variable v(1, para.T)
variable t(1, para.T)
expression lower_bound(1, para.T)
expression D(1, para.T)

for ii=1:para.T
lower_bound(ii) = coe3(ii)*u(ii) + coe4(ii)*v(ii);
D(ii)= coe5(ii)*t(ii) + coe6(ii)*v(ii);
end

maximize(1/para.T*(sum((lower_bound)-D)))

subject to
80 <= u;
40 <= v;
80 <= t;

for jj=1:para.T
pow_pos(norm(traj(jj, :)-para.place_u(1:2)),2)+6400+u0(jj)^2-2*u0(jj)u(jj)<=0;
pow_pos(norm(traj(jj, :)-para.place_R(1:2)),2)+1600+v0(jj)^2-2
v0(jj)v(jj)<=0;
pow_pos(norm(traj(jj, :)-para.place_e(1:2)),2)+6400+t0(jj)^2-2
t0(jj)*t(jj)<=0;
end

for ii=1:para.T
pow_pos(norm(traj(ii+1,:)-traj(ii, :)),2)<=para.Vmax^2;
end

cvx_end

Thanks for your help.

Your problem is dual infeasible and that means your problem does not have finite optimal solution.

Maybe you have forgotten some important constraints.

In case you do not understand what @Erling means in this case by “does not have finite optimal solution”, it is that your problem is unbounded. That is clearly stated in the CVX output “Status: Unbounded”. I.e., the problem has infinite optimal objective value, as stated in “Optimal value (cvx_optval): +Inf”.