Book sequence on convex analysis

In summary, Convex analysis is a branch of mathematics that deals with the study of convex functions and their properties. It has many applications in various fields, including economics, engineering, and computer science, and provides tools for solving optimization problems and understanding complex systems. The key concepts in convex analysis include convex sets, convex functions, subgradients, and convex optimization. It is used in various real-world problems such as portfolio optimization, data fitting, and network routing. Some useful resources for learning about convex analysis are textbooks, online lectures and tutorials, and courses on platforms like Coursera and edX.
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I'm looking for 1-2 rigorous books on convex analysis for someone who already has some exposure to convexity, linear and nonlinear programming in an applied course.

It seems that Rockafellar (Convex Analysis) and Fenchel (Convex Cones, Sets and Functions) is the classic treatment. Is there a more modern exposition? I see a few from a quick Amazon search, but I'm not in a good position to judge:

- Borwein and Lewis, Convex Analysis and Nonlinear Optimization
- Bertsimas, Convex Analysis and Optimization
- Zalinescu, Convex Analysis in General Vector Spaces

Thanks!
 
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What is convex analysis?

Convex analysis is a branch of mathematics that deals with the study of convex functions and their properties. It involves the analysis of convex sets, convex functions, and convex optimization problems.

Why is convex analysis important?

Convex analysis has many applications in various fields, including economics, engineering, and computer science. It provides tools for solving optimization problems, which are prevalent in these fields. It also helps in understanding the behavior of complex systems and provides insights into the structure of solutions.

What are the key concepts in convex analysis?

The key concepts in convex analysis include convex sets, convex functions, subgradients, and convex optimization. Convex sets are sets that contain all points on the line segment joining any two points in the set. Convex functions are functions that have a graph that lies below the line segment joining any two points on the graph. Subgradients are generalizations of derivatives for convex functions, and convex optimization involves finding the minimum of a convex function over a convex set.

What are some real-world examples of convex analysis?

Convex analysis has various applications in real-world problems. Some examples include portfolio optimization in finance, data fitting in machine learning, and network routing in telecommunications. It is also used in control theory, signal processing, and image reconstruction.

What are some useful resources for learning about convex analysis?

Some useful resources for learning about convex analysis include textbooks such as "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe, "Convex Analysis and Optimization" by Dimitri P. Bertsekas, and "Convex Analysis and Nonlinear Optimization" by Jonathan M. Borwein and Adrian S. Lewis. Online resources such as lectures and tutorials on YouTube and courses on platforms like Coursera and edX are also helpful for learning about convex analysis.

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