Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Covers articles on the areas of calculus of variations, control theory, measure theory, functional analysis, differential equations, integralequations, optimization and mathematical programming. Also covers topics related to nonsmooth analysis, generalized differentiability, and set-valued functions.

Convex functions --- Functional analysis --- Convex functions. --- Functional analysis. --- Convexe functies. --- Functions, Convex --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Convex functions

Convex functions. --- Functions. --- Analysis (Mathematics) --- Differential equations --- Mathematical analysis --- Mathematics --- Numbers, Complex --- Set theory --- Calculus --- Functions, Convex --- Functions of real variables --- Fonctions convexes --- Convex functions --- #TCPW W4.0 --- 517.5 --- 517.5 Theory of functions --- Theory of functions

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems. Contents: Classical Abstract Spaces in Functional Analysis Linear Functionals and Linear Operators Common Function Spaces in Applications Differential Calculus in Normed Vector Spaces Minimization of Functionals Convex Functionals Lower Semicontinuous Functionals.

Functional analysis. --- Convex functions. --- Mathematical optimization. --- Existence theorems. --- Differential equations --- Mathematical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Convex --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- System theory. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov’s Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity. The only prerequisites are a background in advanced calculus and linear algebra. Each section ends with exercises, while each chapter ends with comments covering supplementary material and historical information. Many results are new, and the whole book reflects the authors’ own experience, both in teaching and research. About the authors: Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs the Centre for Nonlinear Analysis and Its Applications and also the graduate program in Applied Mathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynamical Systems, and has received several prizes both for research and exposition. Lars Erik Persson is Professor of Mathematics at Luleå University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Luleå, a member of the Swedish National Committee of Mathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from Umeå University in 1974. Dr. Persson has published on interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has received several prizes both for research and teaching.

Convex functions --- Convex functions. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Functions, Convex --- Mathematics. --- Functional analysis. --- Functions of real variables. --- Convex geometry. --- Discrete geometry. --- Real Functions. --- Functional Analysis. --- Convex and Discrete Geometry. --- Functions of real variables --- Discrete groups. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Real variables --- Functions of complex variables --- Geometry --- Combinatorial geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Over the past two decades there have been significant advances in the field of optimization. In particular, convex optimization has emerged as a powerful signal processing tool, and the variety of applications continues to grow rapidly. This book, written by a team of leading experts, sets out the theoretical underpinnings of the subject and provides tutorials on a wide range of convex optimization applications. Emphasis throughout is on cutting-edge research and on formulating problems in convex form, making this an ideal textbook for advanced graduate courses and a useful self-study guide. Topics covered range from automatic code generation, graphical models, and gradient-based algorithms for signal recovery, to semidefinite programming (SDP) relaxation and radar waveform design via SDP. It also includes blind source separation for image processing, robust broadband beamforming, distributed multi-agent optimization for networked systems, cognitive radio systems via game theory, and the variational inequality approach for Nash equilibrium solutions.

Signal processing --- Mathematical optimization --- Convex functions --- Signal processing. --- Mathematical optimization. --- Convex functions. --- Functions, Convex --- Functions of real variables --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)