The paper deals with the problem of maximizing a (nonconvex) homogeneous polynomial over the unit simplex. This program is directly related to the concept of evolutionarily stable strategies in biology. Optimality conditions are studied together with related stability properties. It is shown that generically any local maximizer is an evolutionarily stable strategy. We further extend these results to the case of polynomial optimization over the sphere.
- Evolutionarily stable strategies
- Genericity properties
- Homogeneous polynomials
- Optimization over the simplex
- Stability of maximizers