  We present a model development framework and numerical solution approach to
the general problem-class of packing convex objects into optimized convex
containers. Specifically, here we discuss the problem of packing ovals
(egg-shaped objects, defined here as generalized ellipses) into optimized
regular polygons in $\mathbb{R}^2$. Our solution strategy is based on the use
of embedded Lagrange multipliers, followed by nonlinear (global-local)
optimization. The numerical results are attained using randomized starting
solutions refined by a single call to a local optimization solver. We obtain
credible, tight packings for packing 4 to 10 ovals into regular polygons with 3
to 10 sides in all (224) test problems presented here, and for other similarly
difficult packing problems.
