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Where is the error in my code when describing the model?
Question

Dear all,
Here is the optimization model I want to solve:
while I have written the following code to describe it:
SolverContext context = SolverContext.GetContext();
Model model = context.CreateModel();
Parameter v = new Parameter(Domain.RealNonnegative, "v");
double voltage = 1.0;
v.SetBinding(voltage);
Parameter theta = new Parameter(Domain.RealRange(Math.PI, Math.PI), "theta");
double phaseangle = 0.0;
theta.SetBinding(phaseangle);
model.AddParameters(v, theta);
Decision n = new Decision(Domain.Real, "n");
model.AddDecision(n);
Goal goal = model.AddGoal("voltage_offset", GoalKind.Minimize, Model.Abs(v  1.0));
model.AddConstraint("p_balance", v * Model.Cos(theta)  v * v == 0.1);
model.AddConstraint("q_balance", v * Model.Sin(theta) == 0.1 * (0.8  n));
Solution solution = context.Solve();
Console.Write("{0}", report);
Console.WriteLine("The value of {0} is: {1}", goal.Name, goal.ToString());
When I run the above code, the console will display:
===Solver Foundation Service Report===
Date: 2012/7/31 16:56:53
Version: Microsoft Solver Foundation 3.0.2.10889 Express Edition
Model Name: DefaultModel
Capabilities Applied: LP
Solve Time (ms): 25
Total Time (ms): 84
Solve Completion Status: Infeasible
Solver Selected: Microsoft.SolverFoundation.Solvers.SimplexSolver
Directives:
Microsoft.SolverFoundation.Services.Directive
Algorithm: Primal
Arithmetic: Exact
Variables: 2 > 1 + 0
Rows: 3 > 0
Nonzeros: 2
Eliminated Slack Variables: 0
Basis: Slack
Pivot Count: 0
Phase 1 Pivots: 0 + 0
Phase 2 Pivots: 0 + 0
Factorings: 0 + 0
Degenerate Pivots: 0 (0.00 %)
Branches: 0
The value of voltage_offset is: InfinityIt seems that the model have invoked the simplex solver, however, it is absolutely wrong, since the value of the object function is infinity. Can anybody help me to find the error? Many thanks in advance!
Regards
Tuesday, July 31, 2012 8:58 AM
Answers

Your model is not well defined. As v and theta are parameters, there is no objective left and also the first constraint does not contain any variable. The model is recognized as an LP as the only thing left is the second constraint which is linear in n.
I suspect you are confused about the role of parameters and variables (decisions). If you don't understand those concepts it will be very difficult to implement any model in a correct fashion.
 Erwin Kalvelagen Amsterdam Optimization Modeling Group erwin@amsterdamoptimization.com http://amsterdamoptimization.com 
 Marked as answer by Zhigang Wu Thursday, August 2, 2012 6:23 AM
Tuesday, July 31, 2012 2:59 PM
All replies

Your model is not well defined. As v and theta are parameters, there is no objective left and also the first constraint does not contain any variable. The model is recognized as an LP as the only thing left is the second constraint which is linear in n.
I suspect you are confused about the role of parameters and variables (decisions). If you don't understand those concepts it will be very difficult to implement any model in a correct fashion.
 Erwin Kalvelagen Amsterdam Optimization Modeling Group erwin@amsterdamoptimization.com http://amsterdamoptimization.com 
 Marked as answer by Zhigang Wu Thursday, August 2, 2012 6:23 AM
Tuesday, July 31, 2012 2:59 PM 
Dear Erwin,
Thank you very much, I got the result after I defined v and theta as decisions.
Regards
Zhigang Wu
Thursday, August 2, 2012 6:24 AM