Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization write by Ernö Robert Csetnek. This book was released on 2010-06-30. Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization available in PDF, EPUB and Kindle. The aim of this work is to present several new results concerning duality in scalar convex optimization, the formulation of sequential optimality conditions and some applications of the duality to the theory of maximal monotone operators. After recalling some properties of the classical generalized interiority notions which exist in the literature, we give some properties of the quasi interior and quasi-relative interior, respectively. By means of these notions we introduce several generalized interior-point regularity conditions which guarantee Fenchel duality. By using an approach due to Magnanti, we derive corresponding regularity conditions expressed via the quasi interior and quasi-relative interior which ensure Lagrange duality. These conditions have the advantage to be applicable in situations when other classical regularity conditions fail. Moreover, we notice that several duality results given in the literature on this topic have either superfluous or contradictory assumptions, the investigations we make offering in this sense an alternative. Necessary and sufficient sequential optimality conditions for a general convex optimization problem are established via perturbation theory. These results are applicable even in the absence of regularity conditions. In particular, we show that several results from the literature dealing with sequential optimality conditions are rediscovered and even improved. The second part of the thesis is devoted to applications of the duality theory to enlargements of maximal monotone operators in Banach spaces. After establishing a necessary and sufficient condition for a bivariate infimal convolution formula, by employing it we equivalently characterize the $\varepsilon$-enlargement of the sum of two maximal monotone operators. We generalize in this way a classical result concerning the formula for the $\varepsilon$-subdifferential of the sum of two proper, convex and lower semicontinuous functions. A characterization of fully en.
Fixed-Point Algorithms for Inverse Problems in Science and Engineering
Fixed-Point Algorithms for Inverse Problems in Science and Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed-Point Algorithms for Inverse Problems in Science and Engineering write by Heinz H. Bauschke. This book was released on 2011-05-27. Fixed-Point Algorithms for Inverse Problems in Science and Engineering available in PDF, EPUB and Kindle. "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Multi-Composed Programming with Applications to Facility Location
Multi-Composed Programming with Applications to Facility Location - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multi-Composed Programming with Applications to Facility Location write by Oleg Wilfer. This book was released on 2020-05-27. Multi-Composed Programming with Applications to Facility Location available in PDF, EPUB and Kindle. Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions. As an application, the author derives results for single minmax location problems formulated by means of extended perturbed minimal time functions as well as for multi-facility minmax location problems defined by gauges. In addition, he provides formulae of projections onto the epigraphs of gauges to solve these kinds of location problems numerically by using parallel splitting algorithms. Numerical comparisons of recent methods show the excellent performance of the proposed solving technique. About the Author: Dr. Oleg Wilfer received his PhD at the Faculty of Mathematics of Chemnitz University of Technology, Germany. He is currently working as a development engineer in the automotive industry.
Hilbert Projection Theorem
Hilbert Projection Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert Projection Theorem write by Fouad Sabry. This book was released on 2024-05-04. Hilbert Projection Theorem available in PDF, EPUB and Kindle. What is Hilbert Projection Theorem In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector in a Hilbert space and every nonempty closed convex there exists a unique vector for which is minimized over the vectors ; that is, such that for every How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Hilbert Projection Theorem Chapter 2: Banach space Chapter 3: Inner product space Chapter 4: Riesz representation theorem Chapter 5: Self-adjoint operator Chapter 6: Trace class Chapter 7: Operator (physics) Chapter 8: Hilbert space Chapter 9: Norm (mathematics) Chapter 10: Convex analysis (II) Answering the public top questions about hilbert projection theorem. (III) Real world examples for the usage of hilbert projection theorem in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Hilbert Projection Theorem.
A Mathematical View of Interior-point Methods in Convex Optimization
A Mathematical View of Interior-point Methods in Convex Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Mathematical View of Interior-point Methods in Convex Optimization write by James Renegar. This book was released on 2001-01-01. A Mathematical View of Interior-point Methods in Convex Optimization available in PDF, EPUB and Kindle. Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
