Book sequence on convex analysis

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SUMMARY

The discussion centers on identifying rigorous texts for studying convex analysis, particularly for individuals with prior exposure to convexity and programming. Key recommendations include Rockafellar's "Convex Analysis" and Fenchel's "Convex Cones, Sets and Functions" as foundational texts. Additionally, modern alternatives such as Borwein and Lewis's "Convex Analysis and Nonlinear Optimization," Bertsimas's "Convex Analysis and Optimization," and Zalinescu's "Convex Analysis in General Vector Spaces" are suggested for further exploration.

PREREQUISITES
  • Understanding of convexity concepts
  • Familiarity with linear programming
  • Knowledge of nonlinear programming
  • Basic mathematical rigor in analysis
NEXT STEPS
  • Research "Convex Analysis and Nonlinear Optimization" by Borwein and Lewis
  • Explore "Convex Analysis and Optimization" by Bertsimas
  • Study "Convex Analysis in General Vector Spaces" by Zalinescu
  • Review the foundational concepts in Rockafellar's "Convex Analysis"
USEFUL FOR

Students and professionals in mathematics, optimization researchers, and anyone seeking to deepen their understanding of convex analysis and its applications in linear and nonlinear programming.

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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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