File Name: convex optimization algorithms and complexity .zip
Publisher : arXiv. Description : This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization.
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Many classes of convex optimization problems admit polynomial-time algorithms,  whereas mathematical optimization is in general NP-hard.
Gonzaga 1. Elizabeth W. E-mail: clovis mtm. Postal , Curitiba, PR, Brazil. E-mail: ewkaras ufpr.
Convex Optimization: Algorithms and Complexity
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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Trends Mach. This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Expand Abstract.
Approximation and Optimization
Advanced embedded algorithms are growing in complexity, and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. This paper discusses the formal verification of the ellipsoid method, a convex optimization algorithm, and its code implementation as it applies to receding horizon control. Options for encoding code properties and their proofs are detailed. The applicability and limitations of those code properties and proofs are presented as well. Finally, floating-point errors are taken into account in a numerical analysis of the ellipsoid algorithm.
This course is available with permission as an outside option to students on other programmes where regulations permit. The availability as an outside option requires a demonstration of sufficient background in mathematics and statistics and is at the discretion of the instructor. Some experience with computer programming will be assumed e. The goal of this course is to provide students with a training in foundations of machine learning with a focus on statistical and algorithmic aspects. Students will learn fundamental statistical principles, algorithms, and how to implement and apply machine learning algorithms using the state-of-the-art Python packages such as scikit-learn, TensorFlow, and OpenAI Gym. Weekly problem sets that are discussed in subsequent seminars. The coursework that will be used for summative assessment will be chosen from a subset of these problems.
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Download Citation | Convex Optimization: Algorithms and Complexity | This monograph presents the main complexity theorems Request Full-text Paper PDF.
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