Convex optimization relaxation

  • What are convex relaxation methods?

    One frequently used technique is convex relaxation.
    Relaxation is usually obtained by relaxing some of the constraints of the original problem and meanwhile extending the objective function to the larger space..

  • What is a convex relaxation?

    Convex relaxations are typically built by replacing each non-convex term by a convex underestimator and a concave overestimator.
    From: Computer Aided Chemical Engineering, 2011..

  • What is convex relaxation?

    Relaxation denotes the technique of simply dropping certain constraints from the overall optimization problem.
    Convex relaxation means that upon relaxation the problem becomes convex.Sep 10, 2014.

For some hard problems, we can use convex relaxation techniques to approx- imate the original (hard) problem in a certain way by one that we can solve efficiently. This approximation, which is a convex optimization problem, gives us a bound on the optimal value of the original problem.
For some hard problems, we can use convex relaxation techniques to approx- imate the original (hard) problem in a certain way by one that we can solve efficiently. This approximation, which is a convex optimization problem, gives us a bound on the optimal value of the original problem.

Are convex and concave relaxations possible for deterministic global dynamic optimization?

Based on Scott and Barton’s general ODE relaxation framework [ 60 ], we have proposed a new approach for generating convex and concave relaxations for the solutions of nonconvex parametric ODE systems ( 3 ), for use in deterministic global dynamic optimization

Is convex relaxation based on a duality-based algorithm?

Under very mild assumptions on the dual problem, the authors prove that the minimizers of the original and relaxed problems are the same

Moreover, the relaxed problem easily accommodates all constraints

To solve the convex relaxation, an efficient duality-based algorithm, which incorporates all constraints implicitly, is proposed

Why do we need convex relaxation?

In practice, we often meet complex optimization problems (e

g

, combinatorial optimization problems) whose complexity of computation prevents us to find a global solution in acceptable time

So we need to find good approximations that can be solved much more easily

One frequently used technique is convex relaxation


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