New PDF release: Iterative Optimization in Inverse Problems

By Charles L. Byrne

ISBN-10: 1482222337

ISBN-13: 9781482222333

ISBN-10: 1482222345

ISBN-13: 9781482222340

Iterative Optimization in Inverse Problems brings jointly a couple of very important iterative algorithms for scientific imaging, optimization, and statistical estimation. It accommodates contemporary paintings that has now not seemed in different books and attracts at the author’s substantial examine within the box, together with his lately built category of SUMMA algorithms. on the topic of sequential unconstrained minimization equipment, the SUMMA classification incorporates a wide variety of iterative algorithms renowned to researchers in numerous parts, equivalent to records and photo processing.

Organizing the themes from basic to extra particular, the booklet first offers an summary of sequential optimization, the subclasses of auxiliary-function tools, and the SUMMA algorithms. the subsequent 3 chapters current specific examples in additional aspect, together with barrier- and penalty-function tools, proximal minimization, and forward-backward splitting. the writer additionally makes a speciality of fixed-point algorithms for operators on Euclidean area after which extends the dialogue to incorporate distance measures except the standard Euclidean distance. within the ultimate chapters, particular difficulties illustrate using iterative tools formerly mentioned. such a lot chapters include workouts that introduce new rules and make the e-book appropriate for self-study.

Unifying quite a few possible disparate algorithms, the ebook indicates easy methods to derive new houses of algorithms via evaluating recognized homes of different algorithms. This unifying procedure additionally is helping researchers—from statisticians engaged on parameter estimation to photograph scientists processing scanning info to mathematicians thinking about theoretical and utilized optimization—discover important comparable algorithms in components open air in their expertise.

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Extra info for Iterative Optimization in Inverse Problems

Example text

5 35 36 36 36 39 39 39 40 40 40 41 41 42 42 43 Barrier-function and penalty-function methods are the best known examples of sequential optimization. In their usual formulations neither fits into the AF class of algorithms. However, barrier-function algorithms can be reformulated to fit into the SUMMA class, while penalty-function methods can be converted to barrier-function methods by switching the roles of the objective and penalty functions.

1 Barrier-Function Methods . . . . . . . . . . . . . . . . 2 Penalty-Function Methods . . . . . . . . . . . . . . . Auxiliary-Function Methods . . . . . . . . . . . . . . . . . . . 1 General AF Methods . . . . . . . . . . . . . . . . . . 2 AF Requirements . . . . . . . . . . . . . . . . . . . . 3 Majorization Minimization . . . . . . . . . . . .

In SUM methods the auxiliary functions gk (x) are selected to enforce the constraint that x be in C, as in barrier-function methods, or to penalize violations of that constraint, such as in penalty-function methods. Auxiliary-function (AF) methods, which we shall discuss in some detail, closely resemble SUM methods. In AF methods certain restrictions are placed on the auxiliary functions gk (x) to control the behavior of the sequence {f (xk )}. Even when there are no constraints, the problem of minimizing a real-valued function may require iteration; the formalism of AF minimization can be useful in deriving such iterative algorithms, as well as in proving convergence.

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Iterative Optimization in Inverse Problems by Charles L. Byrne


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