I want to optimize surface area for a fixed volume of an irregular shape. I initially tried to do constrained optimization for an elliptical cone and nothing worked (especially the part for the surface area). Then I tried a sinusoidal cuboid (picture attached) and I ran into problems again. I then used a sigmoid function as the function for solids of revolution for a bottle and had issues as well. Can someone please help me to do the constraint optimization for any of these or any other weird shaped-bottles?
2026-04-02 13:55:27.1775138127
Constrained Optimization for Irregular Shapes
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