Hi,

I'm new to use CPLEX. I got a question about how to add a piecewise nonline constraintto my model. For example, I have 3 overlapped circles c1 to c3, I picked each some parts of each circle, i.e. arc, to form a convex region. Please see the figure below as an example:
I want to constraint the x and y constrainted within the red shadow region. Any help will be appreciated! Thank you!

------------------------------
Qiuchen Qian
------------------------------

#DecisionOptimization

Constraining points to be on or below the blue piecewise linear function is possible. Your shaded region seems to have boundaries composed of circular arcs, though, which cannot be modeled by piecewise linear functions. If that is not what you intended, perhaps you could provide a more detailed explanation or a more detailed diagram.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Original Message:
Sent: Wed November 30, 2022 09:26 AM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Hi,

I'm new to use CPLEX. I got a question about how to add a piecewise nonline constraintto my model. For example, I have 3 overlapped circles c1 to c3, I picked each some parts of each circle, i.e. arc, to form a convex region. Please see the figure below as an example:
I want to constraint the x and y constrainted within the red shadow region. Any help will be appreciated! Thank you!

------------------------------
Qiuchen Qian
------------------------------

#DecisionOptimization

Thanks for the reply, sorry I didn't make it clear. What I want is a nonlinear constraint that describes the red shade, which is formed with 3 arcs. The vertices of the convex region are marked as the red '+' sign. The blue point shows a feasible point (or solution) under this scenairo. Mathcatically, I have:
(x - x₁)² + (y - y₁)² <= r₁²
(x - x₂)² + (y - y₂)² <= r₂²
(x - x₃)² + (y - y₃)² <= r₃²
​
subject to the polar angles of corresponding arcs. Please see the figure below:

------------------------------
Qiuchen Qian
------------------------------

Original Message:
Sent: Wed November 30, 2022 12:14 PM
From: Paul Rubin
Subject: cplex piecewise nonline function constraint

Constraining points to be on or below the blue piecewise linear function is possible. Your shaded region seems to have boundaries composed of circular arcs, though, which cannot be modeled by piecewise linear functions. If that is not what you intended, perhaps you could provide a more detailed explanation or a more detailed diagram.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Original Message:
Sent: Wed November 30, 2022 09:26 AM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Hi,

I'm new to use CPLEX. I got a question about how to add a piecewise nonline constraintto my model. For example, I have 3 overlapped circles c1 to c3, I picked each some parts of each circle, i.e. arc, to form a convex region. Please see the figure below as an example:
I want to constraint the x and y constrainted within the red shadow region. Any help will be appreciated! Thank you!

------------------------------
Qiuchen Qian
------------------------------
#DecisionOptimization

If you want to limit solutions to the intersection of the three disks (the interiors of the three circles), just add all three quadratic inequalities as constraints.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Original Message:
Sent: Wed November 30, 2022 12:47 PM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Thanks for the reply, sorry I didn't make it clear. What I want is a nonlinear constraint that describes the red shade, which is formed with 3 arcs. The vertices of the convex region are marked as the red '+' sign. The blue point shows a feasible point (or solution) under this scenairo. Mathcatically, I have:
(x - x₁)² + (y - y₁)² <= r₁²
(x - x₂)² + (y - y₂)² <= r₂²
(x - x₃)² + (y - y₃)² <= r₃²
​
subject to the polar angles of corresponding arcs. Please see the figure below:

Maybe it is a piecewise quadratic function when we put the feasible point on the arcs. 

------------------------------
Qiuchen Qian

Original Message:
Sent: Wed November 30, 2022 12:14 PM
From: Paul Rubin
Subject: cplex piecewise nonline function constraint

Constraining points to be on or below the blue piecewise linear function is possible. Your shaded region seems to have boundaries composed of circular arcs, though, which cannot be modeled by piecewise linear functions. If that is not what you intended, perhaps you could provide a more detailed explanation or a more detailed diagram.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Original Message:
Sent: Wed November 30, 2022 09:26 AM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Hi,

I'm new to use CPLEX. I got a question about how to add a piecewise nonline constraintto my model. For example, I have 3 overlapped circles c1 to c3, I picked each some parts of each circle, i.e. arc, to form a convex region. Please see the figure below as an example:
I want to constraint the x and y constrainted within the red shadow region. Any help will be appreciated! Thank you!

------------------------------
Qiuchen Qian
------------------------------
#DecisionOptimization

I see, thank you!

------------------------------
Qiuchen Qian
------------------------------

Original Message:
Sent: Wed November 30, 2022 02:03 PM
From: Paul Rubin
Subject: cplex piecewise nonline function constraint

If you want to limit solutions to the intersection of the three disks (the interiors of the three circles), just add all three quadratic inequalities as constraints.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Original Message:
Sent: Wed November 30, 2022 12:47 PM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Thanks for the reply, sorry I didn't make it clear. What I want is a nonlinear constraint that describes the red shade, which is formed with 3 arcs. The vertices of the convex region are marked as the red '+' sign. The blue point shows a feasible point (or solution) under this scenairo. Mathcatically, I have:
(x - x₁)² + (y - y₁)² <= r₁²
(x - x₂)² + (y - y₂)² <= r₂²
(x - x₃)² + (y - y₃)² <= r₃²
​
subject to the polar angles of corresponding arcs. Please see the figure below:

Maybe it is a piecewise quadratic function when we put the feasible point on the arcs. 

------------------------------
Qiuchen Qian

Original Message:
Sent: Wed November 30, 2022 12:14 PM
From: Paul Rubin
Subject: cplex piecewise nonline function constraint

Constraining points to be on or below the blue piecewise linear function is possible. Your shaded region seems to have boundaries composed of circular arcs, though, which cannot be modeled by piecewise linear functions. If that is not what you intended, perhaps you could provide a more detailed explanation or a more detailed diagram.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Original Message:
Sent: Wed November 30, 2022 09:26 AM
From: Qiuchen Qian
Subject: cplex piecewise nonline function constraint

Hi,

I'm new to use CPLEX. I got a question about how to add a piecewise nonline constraintto my model. For example, I have 3 overlapped circles c1 to c3, I picked each some parts of each circle, i.e. arc, to form a convex region. Please see the figure below as an example:
I want to constraint the x and y constrainted within the red shadow region. Any help will be appreciated! Thank you!

------------------------------
Qiuchen Qian
------------------------------
#DecisionOptimization