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Convex Analysis

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Encyclopedia of Mathematical Geosciences

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

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Definition

Convex analysis is a subfield of mathematical optimization, the word meaning of “optimal” is “best” and optimization techniques strive to bring out the best solution. Convex analysis studies the properties of convex functions and convex sets and aims to minimize convex functions over convex sets. It has application in various fields such as automatic control systems, signal processing, deep learning, data analysis and model building, finance, statistics, economics, and so on.

Introduction

In the beginning of 1960s, the works of mathematicians Ralph Tyrrell Rockafellar and Jean Jacques Moreau brought about great advancement in the field of convex analysis. An example for optimization in the field of economics could be profit maximization or cost minimization. As the system complexity increases, analytical solutions become infeasible, and we can reach the optimal solution only through convex analysis and optimization. The goal of convex analysis is to determine x, such that f(...

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Correspondence to Uttam Kumar .

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Solomon, I., Kumar, U. (2022). Convex Analysis. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_67-1

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  • DOI: https://doi.org/10.1007/978-3-030-26050-7_67-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26050-7

  • Online ISBN: 978-3-030-26050-7

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