# How to judge the constraint violation when the objective function is 1?

I have an optimization problem with objective=1 and several constraints. This problem can be solved by CVX. However, there are two questions:

(1) I do not know the constraint violation. How to judge that?

(2) What are the meanings of these symbols (pstep dstep pinfeas dinfeas gap prim-obj )?

It would be greatly appreciated if anyone helps me with this.

## This is the result of running CVX: Calling SDPT3 4.0: 112 variables, 48 equality constraints For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 48
dim. of sdp var = 42, num. of sdp blk = 21
dim. of socp var = 24, num. of socp blk = 6
dim. of linear var = 25

SDPT3: Infeasible path-following algorithms

## number of iterations = 50 primal objective value = 9.30463400e-09 dual objective value = 0.00000000e+00 gap := trace(XZ) = 1.14e-08 relative gap = 1.14e-08 actual relative gap = 9.30e-09 rel. primal infeas (scaled problem) = 1.28e-19 rel. dual " " " = 9.56e-13 rel. primal infeas (unscaled problem) = 0.00e+00 rel. dual " " " = 0.00e+00 norm(X), norm(y), norm(Z) = 2.5e-09, 1.6e+12, 1.6e+12 norm(A), norm(b), norm(C) = 2.6e+02, 1.0e+00, 1.0e+04 Total CPU time (secs) = 0.27 CPU time per iteration = 0.01 termination code = 0 DIMACS: 1.3e-19 0.0e+00 1.3e-12 0.0e+00 9.3e-09 1.1e-08

Status: Solved
Optimal value (cvx_optval): +1

(1) You take the solution, plug into your constraint expressions, evaluate them and then you know by how much they are violated. In other words you can compute the solution quality measures you want yourself once you have the solution.

(2) These are various measures of convergence which are specific to the solver. As an inspiration, for example for Mosek the very similar log output is explained here 13.3 Conic Optimization - Interior-point optimizer โ MOSEK Optimization Toolbox for MATLAB 10.0.46