Non convex optimization np hard

  • Are non-convex optimization problems NP-hard?

    Nonconvex optimization is NP-hard, even the goal is to compute a local minimizer.May 27, 2016.

  • What does non-convex optimization mean?

    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 NP-hard optimization?

    You can easily define NP-hard optimisation problems: We call a decision problem D NP-hard if any decision problem in NP can be reduced to D in polynomial time.
    And we can use the same definition for any problem P: P is NP-hard if any decision problem in NP can be reduced to P in polynomial time..

  • Mini-Batch Gradient Descent
    Like SGD, mini-batch SGD does not guarantee finding the global minimum in non-convex optimization problems. mini SGD is the hybrid model of the SGD and BGD which involves the speed of the SGD and accuracy of BGD to solve the optimization problems.
Mar 26, 2018Yes, non-convex optimization is NP-hard. For a simple proof, consider the following reduction from Subset-Sum. The Subset-Sum problem asks  If a convex optimization problem can be NP-Hard, in what sense are Mixed integer non convex optimization problemWhich non convex optimization algorithms guarantee a global optima?More results from cs.stackexchange.com
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.
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.

Are non-convex optimization problems NP-complete?

In the context of non-convex optimization problems, one cannot but mention the class of combinatorial optimization problems as graph problems

Basically, most of these problems are NP-complete, but despite this, there are effective approaches and ways to solve them

Let us consider a closer look at the MAX-CUT problem

Is the NP-hard problem a global solution of a non-convex problem?

Following , we consider an example that illustrates that the problem of finding the exact global solution of a non-convex problem is NP-hard

To that end, we consider the minimization problem

What are tractable non-convex optimization problems?

2 3

3 Geometry of Non-Convex Optimization Problems In one of the latest surveys , the authors want to distinguish a class of tractable non-convex problems, which have certain properties of symmetry

They highlight non-convex optimization problems with rotational symmetry and discrete symmetry

Nonconvex optimization is NP-hard, even the goal is to compute a local minimizer. In applied disciplines, however, nonconvex problems abound, and simple algorithms, such as gradient descent and alternating direction, are often surprisingly effective.

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