topic Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint? in SAS/IML Software and Matrix Computations

Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

Emara — Sat, 12 Jan 2013 12:43:31 GMT

Dear all,

My non linear optimization syntax is running without errors however, when i substitute with the optimal parameter estimates in the objective function, I did't get the optimal objective value. Also, the optimal parameter estimates don't satisfy my constraint. I attached the output I got, I don't figure out any problems or errors in my syntax, Any help or suggestions?

Emara

Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

1zmm — Sat, 12 Jan 2013 15:07:27 GMT

Could you specify your two-parameter nonlinear model?

According to your output,

X1 X2 Value of objective function

Starting parameter values: 0.798 0.150 3.4654

Optimized parameter values: 0 0.880851 3.45307

The constraint violation occurs only with the optimized value of X1, which is minimally different from zero but negative (not meeting your lower bound constraint). However, this violation of the constraint is minimal.

The facts that the optimized values of X1 and X2 differ so much from the starting parameter values, that the optimized value for one of these values is on the constraint boundary, and that the value of the objective function changes so minimally imply that many parameter values are consistent with your data, that the objective function "space" is basically flat, and that you probably need more data to distinguish among these values to find a global minimum. What happens to the values of the objective function when you remove or widen the constraints?

Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

Emara — Sat, 12 Jan 2013 17:47:59 GMT

Thanks alot for ur help, I attached the syntax containing my model. I tried to run the syntax without the consraint as you mentioned and i got the following output:

Optimization Start

Active Constraints 0 Objective Function 3.469302357

Objective Std Dev Restart

Function Active Objective Function of Simplex Vertex Simplex

Iter Restarts Calls Constraints Function Change Values Length Size

1 0 20 2 3.45151 0.0125 0.00540 1.000 0.200

Optimization Results

Iterations 1 Function Calls 22

Restarts 0 Active Constraints 2

Objective Function 3.4657027053 Std Dev of Simplex Values 0.0053965381

Deltax 1 Size 0.1995

All parameters are actively constrained. Optimization cannot proceed.

NOTE: At least one element of the (projected) gradient is greater than 1e-3.

Optimization Start

Active Constraints 0 Objective Function 3.469302357

Objective Std Dev Restart

Function Active Objective Function of Simplex Vertex Simplex

Iter Restarts Calls Constraints Function Change Values Length Size

1 0 20 2 3.45151 0.0125 0.00540 1.000 0.200

Optimization Results

Iterations 1 Function Calls 22

Restarts 0 Active Constraints 2

Objective Function 3.4657027053 Std Dev of Simplex Values 0.0053965381

Deltax 1 Size 0.1995

All parameters are actively constrained. Optimization cannot proceed.

NOTE: At least one element of the (projected) gradient is greater than 1e-3.

Optimization Results

Parameter Estimates

Active

Bound

N Parameter Estimate Constraint

1 X1 0 Lower BC

2 X2 1.000000 Upper BC

Value of Objective Function = 3.4657027053

The Lagrange multipliers for active lower bounds are equal to the corresponding gradient

element; for upper bounds, they are equal to the negative gradient element.

Tthanks,

Emara

Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

1zmm — Sat, 12 Jan 2013 21:35:49 GMT

Obviously, that didn't work. When I tried your PROC IML program you sent, the program took a very long time and did NOT converge. I tried reducing the number of iterations and changing the input data, but the problem seems to be with the slow convergence of the Nelder-Mead simplex method on your problem. Do you have previously published input data for your problem that are known to converge to known solutions using this method? If so, try to see if you obtain these solutions using these input data. Otherwise, see if you can recast your problem so that another optimization method might work with it. What is the purpose of this optimization?

Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

Rick_SAS — Sun, 13 Jan 2013 01:49:20 GMT

For previous threads associated with earlier stages of this project/program, see

https://communities.sas.com/thread/38604

and

https://communities.sas.com/thread/39637

Re: Why Optimization results don't produce the optimal objective value and don't satisfy the constraint?

Emara — Sun, 13 Jan 2013 19:49:29 GMT

I run my model once again and it took 10 minutes to get the output i attached before, my questions are:

1-does the output indicate problems in the model?does the output indicate that my constraint is violated or that the optimal parameter estimates won't result in the displayed optimal objective value?

2-why the optimal parameter estimates don't satisfy the constraints and don't result in the optimal objective value?

3-why every time i run my model i get different answers?

4-Does this part of the output indicate that the constraint is satisfied? if so, why when i substitute with the optimal values in my constraint, i find that the constraint is not satisfied?

Values of Nonlinear Constraints

Constraint Residual

[ 1 ] 0 Active NLEC

Waiting for your reply,

Emara