What is non convex optimization

  • What is convex and non convex?

    A polygon is convex if all the interior angles are less than 180 degrees.
    If one or more of the interior angles is more than 180 degrees the polygon is non-convex (or concave).
    All triangles are convex It is not possible to draw a non-convex triangle..

Are non-convex problems hard to solve?

Many practical problems of importance are non-convex, and most non-convex problems are hard (if not impossible) to solve exactly in a reasonable time

Indeed, most non-convex problems suffer from the ‘‘curse’’ of local minima, which may trap algorithms into a spurious solution

How important is non-convex optimization?

H umans have been enjoying convex optimization (CO) for many years compared to the few contexts where they had to deal with non-convex optimization (NCO)

However, over the last decade, non-convex optimization became more crucial and important than before


Categories

Convex optimization of functions
Opposite of optimizing
Convex optimization permutation
Convex optimization for electrical engineering
Convex optimization
Convex optimization by stephen boyd and lieven vandenberghe
Bandit convex optimization towards tight bounds
Optimization under constraints
Convex optimization and applications
Convex optimization and concave
Convex optimization and geometry
Convex optimization and dual problem
Convex optimization and linear algebra
Convex optimization and cost function
Convex optimization and tensors
Convex optimization and derivatives
Convex optimization and operation research
Large-scale convex optimization via monotone operators
Non convex optimization
Convex optimization-based beamforming