MATLAB: Inequality constraints for optimizer

linear inequality constraintsoptimization

Hello,

I want the solution (x,y) of my optimization problem to belong to a specific region of the search-space as depicted below. This region can have an arbitrary shape.

1st case: The red region is known, by knowing the equation of each red line (segment). Is it possible to create a set of inequalities?

2nd case: The red region is known, by knowing the coordinates of all points of its perimeter. Is it possible to create a set of inequalities?

Thanks in advance.

Best Answer

Assuming the region is convex, the answer is yes in both cases. Otherwise, the answer is no - inequalitites will not be enough to specify a nonconvex polygon.

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MATLAB: Delaunay special constraints not being part of the triangulation

Trivial. At least if the triangles are not allowed to cross that internal boundary.

Simply create a polygon that describes the boundary, as a list of edges. Include those points in the set of points for your triangulation.

Set that list of edges from the polygon as constrained edges, and form a constrained triangulation.

No triangle will be able to CROSS one of those edges now, although there will be triangles INSIDE that constrained region. Now just delete any triangle from the tessellation that has all three vertices on the constraint polygon. What remains will have edges on the polygon, but none that can cross it.

You will not be able to insist that nothing even touch that region using constraints, while allowing edges to otherwise come arbitrarily close. The best you can do is to create a polygon as I suggested, but first move each vertex slightly outside. Thus, you must create a polygon that entirely contains your constraint domain yet lies some finite distance outside of the constraint region, then use the scheme I suggested above.

MATLAB: Help me plot 3D graph like these picture

Try this

x = linspace(0,1,500);
y = linspace(0,1,500);
[Xg, Yg] = meshgrid(x, y);
mask = Yg > sqrt(Xg);
Zg = 1 - Yg;
Zg(~mask) = nan;
surf(Xg, Yg, Zg, 'FaceColor', 'b', 'FaceAlpha', 0.4, 'EdgeColor', 'none')
hold on
y = linspace(0,1,500);
z = linspace(0,1,500);
[Yg, Zg] = meshgrid(y, z);
mask = Yg < 1 - Zg;
Xg = Yg.^2;
Xg(~mask) = nan;
surf(Xg, Yg, Zg, 'FaceColor', 'b', 'FaceAlpha', 0.4, 'EdgeColor', 'none')
view(gca,[115 45]);

Best Answer

Related Solutions

MATLAB: Delaunay special constraints not being part of the triangulation

MATLAB: Help me plot 3D graph like these picture

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