Good Books on Optimization Theory

In summary, the conversation discusses the topic of optimization theory and the desire to self-study the subject. The speaker mentions the various sub-fields of optimization theory, including maximizing and minimizing continuous functions, optimal statistical decisions, and the design of experiments. They also express interest in books on these topics and ask for recommendations.
  • #1
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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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  • #2
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."
 
  • #3
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.
 

1. What is optimization theory?

Optimization theory is a branch of mathematics that deals with finding the best solution to a problem within a set of constraints. It aims to maximize or minimize a specific objective function by using various mathematical techniques.

2. Why is optimization theory important?

Optimization theory is important because it has numerous real-world applications in fields such as economics, engineering, and computer science. It allows us to find the most efficient and effective solutions to complex problems, leading to improved decision-making and resource allocation.

3. What are some common techniques used in optimization theory?

Some common techniques used in optimization theory include linear programming, nonlinear programming, dynamic programming, and convex optimization. Other methods such as genetic algorithms and simulated annealing are also used in certain cases.

4. Can optimization theory be applied to real-life situations?

Yes, optimization theory can be applied to a wide range of real-life situations, including resource allocation, production planning, transportation and logistics, and financial planning. It is a valuable tool for making optimal decisions in complex systems.

5. Are there any good books on optimization theory?

Yes, there are many good books on optimization theory that cover various topics and techniques in depth. Some popular titles include "Introduction to Optimization" by Edwin K. P. Chong and Stanislaw H. Zak, "Nonlinear Programming: Theory and Algorithms" by Mokhtar S. Bazaraa, Hanif D. Sherali, and C. M. Shetty, and "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe.

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