Large-scale convex optimization via monotone operators

  • How does convex optimization work?

    With recent advancements in computing and optimization algorithms, convex programming is nearly as straightforward as linear programming..

  • Is convex optimization hard?

    Prerequisites.
    You should have good knowledge of linear algebra and exposure to probability.
    Exposure to numerical computing, optimization, and application fields is helpful but not required; the applications will be kept basic and simple..

  • Is convex optimization hard?

    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..

  • What is an example of a convex optimization problem?

    With recent advancements in computing and optimization algorithms, convex programming is nearly as straightforward as linear programming..

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. Google BooksOriginally published: November 16, 2022Authors: Ernest K. Ryu and Wotao Yin

Are subdifferentials maximally monotone operators?

We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents

In particular, we study new transformations which map proximity operators to proximity operators, and establish connections with self-dual classes of firmly nonexpansive operators

Is convex optimization first-order?

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators

What is monotone operator theory?

Monotone operator theory is fundamental to the development of modern algorithms for large-scale convex optimization


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