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Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author's objective is to provide the foundations of theory and algorithms of nonlinear optimization, as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization
– gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation
– includes a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression
– studies applications both theoretically and algorithmicatly, illustrating concepts such as duality and
– contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares.
Python and MatLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MatLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader’s understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MatLAB examples.
Table of contents:
Mathematical Preliminaries
Optimality Conditions for Unconstrained Optimization
Least Squares
The Gradient Method
Newton’s Method
Convex Sets
Convex Functions
Convex Optimization
Optimization over a Convex Set
Optimality Conditions for Linearly Constrained Problems
The KKT Conditions
Duality