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Convexity is one of the most useful characteristics that can be attributed to an object. Convex spaces play a major role in understanding topological structures. Convexity has lead to fundamental tools in graph theory. In optimization, convexity is one of few general frameworks that guarantees global optimality. Indeed, the value of convexity may be best gleaned by the fact that numerous generalization of convexity have been proposed.

This special topic issue of AIMS Mathematics focuses on convexity, with an emphasis on algorithms and applications. The special issue brings together results related to convexity and conveys the wide range of its application areas.  The issue presents a collection of original research articles from leading experts in the field, covering topics such as convex optimization, nonsmooth analysis, duality theory, and generalizations of convexity.  Novel applications are welcomed from a wide variety of areas, such as data science, finance, machine learning, signal processing, image processing, robotics, scheduling, and engineering.  The issue provides a comprehensive overview of recent developments in the theory and applications of convexity, and aims to stimulate further research in this important area of mathematics and computer science.

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