Convex optimization polynomial time

  • Is convex optimization polynomial time?

    Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard..

  • Is convex problem NP-hard?

    There are special cases of convex problems that can be solved in polynomial time, e.g. a convex QP defined over a simplex.
    In general, however, convex programming is NP-hard.
    However, NP-hard by no means means unsolvable..

  • There are special cases of convex problems that can be solved in polynomial time, e.g. a convex QP defined over a simplex.
    In general, however, convex programming is NP-hard.
    However, NP-hard by no means means unsolvable.
Apr 2, 2012No, this is not true (unless P=NP). There are examples of convex optimization problems which are NP-hard. Several NP-hard combinatorial  Computational complexity of unconstrained convex optimisationIs non-convex optimisation really in NP class? - MathOverflowMore results from mathoverflow.net

Does convex optimization converge in time polynomial?

In fact, for a large class of convex optimization problems, the method converges in time polynomial in

The interior-point approach is limited by the need to form the gradient and Hessian of the function above

For extremely large-scale problems, this task may be too daunting

Does Newton's method converge in time polynomial?

For a large class of convex optimization problems, the function is self-concordant, so that we can safely apply Newton's method to the minimization of the above function

In fact, for a large class of convex optimization problems, the method converges in time polynomial in

What is the algorithmic theory of convex optimization over discrete sets?

Abstract We develop an algorithmic theory of convex optimization over discrete sets

Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension

No, this is not true (unless P=NP). There are examples of convex optimization problems which are NP-hard. Several NP-hard combinatorial optimizatio...Best answer · 49

You should check out Boyd-Vanderberghe's convex optimization, available for free on Boyd's web page at Stanford. This has a discussion of the "easy...6

For many cases, Yes (but see Dima's and Brian's answers), by work of Yu. Nesterov, A. Nemirovski, as summarized in their book Interior-Point Po...4

If I understand correctly, interior-point algorithms require the objective and constraint functions to have a certain amount of smoothness.2

,This question concerns continuous convex minimization. However, the motivating example is the classic binary knapsack problemmax…

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