Convex optimization epfl

  • What is convex set in optimization?

    A convex set is a collection of points in which the line AB connecting any two points A, B in the set lies completely within the set..

  • What is the use of convex optimization in machine learning?

    Convex optimization is used in many machine learning applications, including linear regression, logistic regression, support vector machines, and neural networks.
    Gradient descent can effectively handle the optimization problem, which is a convex optimization problem..

  • If the bounds on the variables restrict the domain of the objective and constraints to a region where the functions are convex, then the overall problem is convex.
  • Some real-life examples of convex optimization problems include the following: Scheduling of flights: Flight scheduling is an example convex optimization problem.
    It involves finding flight times that minimize costs like fuel, pilot/crew costs, etc. while maximizing the number of passengers.
Convex optimization is a fundamental branch of applied mathematics that has applications in almost all areas of engineering, the basic sciences and economics.
The course primarily focuses on techniques for formulating decision problems as convex optimization models that can be solved with existing software tools. The 

Does smooth convex optimization guarantee global convergence to a global minimum?

4

4 Smooth convex optimization All convergence results presented so far have a local nature and do not guarantee global convergence to a global minimum

More can be said if the target func- tional is convex

What is convex optimization problem?

One of the case of it is convex optimization problem which is a problem of minimizing convex functions over convex sets

17' Inception (-v4, -ResNet) (writing ) Keras (writing

) When we solve machine learning problem, we have to optimize a certain objective function

Which function is called convex if 2 0 1?

De nition 4

18 A function f : Rn ! R is called convex if 2 [0; 1]

It is often quite tedious to verify the condition (4

32)

It is much easier to check convexity for (twice) continuously di erentiable functions


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