Non convex optimization book

  • Is non convex NP hard?

    Yes, non-convex optimization is NP-hard.
    For a simple proof, consider the following reduction from Subset-Sum.
    The Subset-Sum problem asks whether there is a subset of the input integers a1,…,an which sums to zero..

  • Is non-convex NP hard?

    Yes, non-convex optimization is NP-hard.
    For a simple proof, consider the following reduction from Subset-Sum.
    The Subset-Sum problem asks whether there is a subset of the input integers a1,…,an which sums to zero..

  • What is non-convex Optimisation?

    A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below.
    Such a problem may have multiple feasible regions and multiple locally optimal points within each region..

  • What is the difference between convex and nonconvex?

    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..

  • 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.
Jul 8, 2022Deterministic global optimization: theory, methods and applications. Vol. 37. Springer Science & Business Media, 2013. Horst, Reiner, and Hoang 

Does update rule obey nonconvex optimization?

The update rule (xt+1 = xt − ηg(xt)) with η = μ and x0 ∈ Bδ(xopt) obeys nonconvex optimization! What does the curvature behave like, at least locally around the global minimizer?

What are some good non-convex optimization books?

There are not many books which specifically cater to non-convex optimization, this book is one of the first dedicated texts I could find

But then again, this isn't exactly an easy read

Happy learning

Optimization by Vector Space Methods by Luenbeger, and Non-Linear Programming by Bertsekas

What is non-convex optimization for machine learning?

Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning

It introduces the rich literature in this area, as well as equipping the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems


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