Decision Optimization

Since your decision variables are integer you could use CPOptimizer within CPLEX:

using CP; dvar int x in -1..1;dvar int y in -1..1; minimize    5*x*x + 5*y*y + 4*x*y; subject to {   x*x + y*y == 1;} execute {    writeln("Results:");    writeln("-----------------");    writeln("x = ", x);    writeln("y = ", y);    writeln("objective = ", 5*x*x + 5*y*y + 4*x*y);  }    

Since your decision variables are integer you could use CPOptimizer within CPLEX:

using CP; dvar int x in -1..1;dvar int y in -1..1; minimize    5*x*x + 5*y*y + 4*x*y; subject to {   x*x + y*y == 1;} execute {    writeln("Results:");    writeln("-----------------");    writeln("x = ", x);    writeln("y = ", y);    writeln("objective = ", 5*x*x + 5*y*y + 4*x*y);  }    

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[Alex] [Fleischer]
[Data and AI Technical Sales]
[IBM]

Original Message:
Sent: Wed November 20, 2024 04:53 AM
From: Fatin Nur Amirah Mahamood
Subject: Error: CPLEX(default) cannot extract expression

------------------------------
Fatin Nur Amirah Mahamood
------------------------------

Thank you for your response. However, I need to clarify that my decision variable (dvar) should be in float. The expected result is x=-1/sqrt(2) , y=1/sqrt(2). This result matches both the textbook example and my manual calculations, as well as results obtained using Python's scipy library (via the Lagrange method).

From my understanding, "using cp;" does not allow for float dvar. Is there an alternative approach to solving this problem?

Additionally, I came across this statement in the documentation:

I also verified that my constraint is not convex. Does this imply that my function cannot be solved using CPLEX?

Thank you for your guidance.

------------------------------
Fatin Nur Amirah Mahamood

Original Message:
Sent: Wed November 20, 2024 12:00 PM
From: ALEX FLEISCHER
Subject: Error: CPLEX(default) cannot extract expression

Since your decision variables are integer you could use CPOptimizer within CPLEX:

using CP; dvar int x in -1..1;dvar int y in -1..1; minimize    5*x*x + 5*y*y + 4*x*y; subject to {   x*x + y*y == 1;} execute {    writeln("Results:");    writeln("-----------------");    writeln("x = ", x);    writeln("y = ", y);    writeln("objective = ", 5*x*x + 5*y*y + 4*x*y);  }    

------------------------------
[Alex] [Fleischer]
[Data and AI Technical Sales]
[IBM]

Original Message:
Sent: Wed November 20, 2024 04:53 AM
From: Fatin Nur Amirah Mahamood
Subject: Error: CPLEX(default) cannot extract expression

------------------------------
Fatin Nur Amirah Mahamood
------------------------------

My response was crafted with AI assistance, tailored to provide detailed and actionable guidance for your query.

The error occurs because IBM CPLEX does not allow certain types of constraints, particularly quadratic equalities, in mixed-integer programming problems (dvar int). Quadratic equality constraints like x*x + y*y == 1 cannot be directly handled with integer decision variables.

Piecewise Approximation: If the enumeration approach isn't feasible (e.g., larger ranges), approximate the circle using a combination of constraints or lookup tables.

Use a Constraint Programming (CP) Engine

The CP engine (using CP;) supports certain types of logical constraints better, such as enumerations, but it still won't handle the quadratic equality directly. Reformulate the problem to use CP if enumeration or constraints like "or" conditions are more natural.