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The book presents a comprehensive framework for various numerical optimization methods through its "reduce-or-retreat" approach, which balances reducing the objective at trial points with retreating to closer alternatives. It aligns derivative-based methods, fostering the development of new techniques and theoretical insights. The author introduces generalizations for non-smooth objectives and examines convergence through a novel notion of stationarity. By exploring descent conditions and situational convergence, the text broadens traditional analyses and connects diverse minimization strategies.
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Stationarity and Convergence in Reduce-or-Retreat Minimization, Adam B. Levy
- Language
- Released
- 2012
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- (Paperback)
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- Title
- Stationarity and Convergence in Reduce-or-Retreat Minimization
- Language
- English
- Authors
- Adam B. Levy
- Publisher
- Springer New York
- Released
- 2012
- Format
- Paperback
- Pages
- 68
- ISBN13
- 9781461446415
- Category
- Mathematics, Computers, IT, Programming
- Description
- The book presents a comprehensive framework for various numerical optimization methods through its "reduce-or-retreat" approach, which balances reducing the objective at trial points with retreating to closer alternatives. It aligns derivative-based methods, fostering the development of new techniques and theoretical insights. The author introduces generalizations for non-smooth objectives and examines convergence through a novel notion of stationarity. By exploring descent conditions and situational convergence, the text broadens traditional analyses and connects diverse minimization strategies.