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About 8,209 papers for “unconstrained optimization”

Unconstrained Optimization

Wiley series in probability and statistics · 1989

This chapter includes the following topics: Introduction Terminology Second-Derivative (Modified Newton) Methods First-Derivative Methods Methods without Derivatives Methods for Nonsmooth Functions Summary

Cited by 1

Unconstrained Optimization

Raphael T. Haftka, Zafer Gürdal, Manohar P. Kamat · Solid mechanics and its applications · 1990

Cited by 5

Unconstrained Optimization

2004

A random search algorithm for unconstrained local nonsmooth optimization is described.The algorithm forms a partition on R n using classification and regression trees (CART) from statistical pattern recognition.The CART partition defines desirable subsets where the objective function f is relatively low, based on previous sampling, from which further samples are drawn directly.Alternating between partition and sampling phases provides an effective method for nonsmooth optimization.The sequence of iterates {z k } is shown to converge to an essential local minimizer of f with probability one under mild conditions.Numerical results are presented to show that the method is effective and competitive in practice.

Cited by 0

Unconstrained Optimization

Ruye Wang · Cambridge University Press eBooks · 2025

Emphasizing how and why machine learning algorithms work, this introductory textbook bridges the gap between the theoretical foundations of machine learning and its practical algorithmic and code-level implementation. Over 85 thorough worked examples, in both Matlab and Python, demonstrate how algorithms are implemented and applied whilst illustrating the end result. Over 75 end-of-chapter problems empower students to develop their own code to implement these algorithms, equipping them with hands-on experience. Matlab coding examples demonstrate how a mathematical idea is converted from equations to code, and provide a jumping off point for students, supported by in-depth coverage of essential mathematics including multivariable calculus, linear algebra, probability and statistics, numerical methods, and optimization. Accompanied online by instructor lecture slides, downloadable Python code and additional appendices, this is an excellent introduction to machine learning for senior undergraduate and graduate students in Engineering and Computer Science.

Cited by 0

Unconstrained Optimization

Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty · 2005

This chapter contains sections titled: Line Search Without Using Derivatives Line Search Using Derivatives Some Practical Line Search Methods Closedness of the Line Search Algorithmic Map Multidimensional Search Without Using Derivatives Multidimensional Search Using Derivatives Modification of Newton's Method: Levenberg–Marquardt and Trust Region Methods Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods Subgradient Optimization Exercises Notes and References

Cited by 1

Unconstrained Optimization

Hime Oliveira, Lester Ingber, Antonio Petraglia et al. · Intelligent systems reference library · 2012

Cited by 1

Unconstrained Optimization

Guido Buzzi‐Ferraris, Flavio Manenti · 2013

This chapter contains sections titled: Introduction Heuristic Methods Gradient-Based Methods Conjugate Direction Methods Newton's Method Modified Newton Methods Quasi-Newton Methods Narrow Valley Effect Stop Criteria BzzMath Classes for Unconstrained Multidimensional Minimization Case Study Tests

Cited by 0

Unconstrained Optimization

Ashok D. Belegundu, Tirupathi R. Chandrupatla · Cambridge University Press eBooks · 2019

Organizations and businesses strive toward excellence, and solutions to problems are based mostly on judgment and experience. However, increased competition and consumer demands require that the solutions be optimum and not just feasible. Theory leads to algorithms. Algorithms need to be translated into computer codes. Engineering problems need to be modeled. Optimum solutions are obtained using theory and computers, and then interpreted. Revised and expanded in its third edition, this textbook integrates theory, modeling, development of numerical methods, and problem solving, thus preparing students to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multi-objective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate courses in optimization design and for practicing engineers.

Cited by 1