Good Books on Optimization Theory

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SUMMARY

The discussion centers on identifying key literature in optimization theory, specifically focusing on the maximization and minimization of continuous functions and optimal statistical decisions. Participants emphasize the importance of defining specific sub-fields within optimization, such as Integer Programming and The Design of Experiments. Recommendations for books on these topics are sought to facilitate self-study. The consensus is that a solid understanding of these areas is crucial for effectively addressing various optimization problems.

PREREQUISITES
  • Understanding of continuous functions and their optimization
  • Familiarity with Integer Programming concepts
  • Knowledge of statistical decision-making processes
  • Basic principles of experimental design
NEXT STEPS
  • Research "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe
  • Explore "Integer Programming" by Laurence A. Wolsey
  • Study "Optimal Statistical Decisions" by Harold Hotelling
  • Learn about "The Design of Experiments" by Ronald A. Fisher
USEFUL FOR

Students, researchers, and professionals in mathematics, statistics, and operations research who are looking to deepen their understanding of optimization theory and its applications.

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IS there a standard in the field for books on optimization theory. I'd like to possibly do a self-study on the subject. Thanks for the info!
 
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You'll have to be more specific about the subject that you want to study. "Optimization theory" could be the study of how to maximize and minimize continuous functions, or the sutdy of how to maximize and minimize functions defined only on the integers ("Integer Programming"), or the study of how to minimize risk ( as defined mathematically) in situations involving probability ("Optimal Statistical Decisions"), or the study of how to plan experiments for fitting multinomial models to data ("The Design Of Experiments").

One of my professors said "Every problem can be phrased as an optimization problem."
 
I suppose the sub-fields I'd be interested in involve maximization and minimization of continuous functions using an associated cost function of all of the parameters. Optimal statistical decisions also sounds interesting. Any references to good books on these topics would be much appreciated.
 

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