Best Reference Books – Generalized Convexity and Variational Inequalities

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We have compiled the list of Top 10 Best Reference Books on Generalized Convexity and Variational Inequalities subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Generalized Convexity and Variational Inequalities along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Generalized Convexity and Variational Inequalities subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Generalized Convexity and Variational Inequalities" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization” by Qamrul Hasan Ansari and C S Lalitha

“Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization” Book Review: This book covers the concepts of generalised convexity, nonsmooth variational inequalities, and nonsmooth optimization, variational inequalities problems defined by bifunction under one roof. It talks in detail about the generalised convexity and monotonicity for both differentiable and non differentiable cases. Concepts of bifunction and Clarke subdifferential are introduced in case of non-differentiable cases. It also talks about variational inequalities and optimization problems in smooth and nonsmooth settings viz., existence and uniqueness criteria for a variational inequality, the gap function accompanied with it, and numerical methods to solve it. It also analyses the characterizations of a solution set of an optimization problem and inspects variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Finally it talks about the integrating results on convexity, monotonicity, and variational inequalities.

2. “Generalized Convexity, Generalized Monotonicity: Recent Results (Nonconvex Optimization and Its Applications)” by Jean-Pierre Crouzeix and Juan Enrique Martinez Legaz

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“Generalized Convexity, Generalized Monotonicity: Recent Results (Nonconvex Optimization and Its Applications)” Book Review: This book talks about the recent result of generalized convexity and generalized monotonicity. Chapters covered in this book are: Are Generalized Derivatives Useful for Generalized Convex Functions?, Stochastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues, Error Bounds for Convex Inequality Systems, Applying Generalised Convexity Notions to Jets, Quasiconvexity via Two Step Functions, On Limiting Fréchet ε-Subdifferentials, Convexity Space with Respect to a Given Set, A Convexity Condition for the Nonexistence of Some Anti Proximal Sets in the Space of Integrable Functions, Characterizations of ρ-Convex Functions, Characterizations of Generalized Convexity and Generalized Monotonicity, A Survey, Quasi Monotonicity and Pseudo Monotonicity in Variational Inequalities and Equilibrium Problems, Quasi Monotonicity and Pseudo Monotonicity in Variational Inequalities and Equilibrium Problems, Variational Inequalities and Pseudomonotone Functions: Some Characterizations, Simplified Global Optimality Conditions in Generalized Conjugation Theory, Duality in DC Programming, Recent Developments in Second Order Necessary Optimality Conditions, Higher Order Invexity and Duality in Mathematical Programming, Fenchel Duality in Generalized Fractional Programming, The Notion of Invexity in Vector Optimization: Smooth and Nonsmooth Case, Quasiconcavity of Sets and Connectedness of the Efficient Frontier in Ordered Vector Spaces, Multiobjective Quadratic Problem: Characterization of the Efficient Points, Generalized Concavity for Bicriteria Functions and Generalized Concavity in Multiobjective Programming.

3. “Generalized Convexity and Optimization: Theory and Applications (Lecture Notes in Economics and Mathematical Systems)” by Alberto Cambini and Laura Martein

“Generalized Convexity and Optimization: Theory and Applications (Lecture Notes in Economics and Mathematical Systems)” Book Review: This book talks about the theory and applications of generalized convexity and optimization. It encompasses the following chapters: Convex Functions, Non-Differentiable Generalized Convex Functions, Differentiable Generalized Convex Functions, Optimality and Generalized Convexity, Generalized Convexity and Generalized Monotonicity, Generalized Convexity of Quadratic Functions, Generalized Convexity of Some Classes of Fractional Functions and Sequential Methods for Generalized Convex Fractional Programs. Solutions to the exercise problems are also available at the end of the book.

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4. “Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture” by Prem K Kythe

“Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture” Book Review: This book suits the graduate students pursuing analytical research on the topics and researchers working on related domains of complex analysis in one or multiple complex variables. The book first talks about the theory of analytic functions, univalent functions, and conformal mapping before eventually covering various theorems related to the area principle and discussing Lowner theory. The author also discusses about the Schiffer’s variation method, bounds for 4rth and higher-order coefficients, numerous subclasses of univalent functions, generalized convexity and the class of α-convex functions, and numerical estimates of the coefficient problem. The book further summarises the orthogonal polynomials, explores the de Branges theorem, and addresses current and emerging developments through the de Branges theorem.

5. “Restricted-Orientation Convexity (Monographs in Theoretical Computer Science. An EATCS Series)” by Eugene Fink and Derick Wood

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“Restricted-Orientation Convexity (Monographs in Theoretical Computer Science. An EATCS Series)” Book Review: This book is designed for research analysts on the topics of restrict oriented convexity. The book starts off with briefly introducing the concepts of convex sets and then eventually discusses the restricted orientations polynomials, restricted orientation convexity in multidimensional space and review of standard convexity, related notions of convex hulls and kernels, ortho-convexity and strong ortho-convexity, topological generalization of convex sets. Main results, comparison of different convexities and conjectures are given at the end of the book.

6. “Some Topics in Generalized Convexity” by Waqquas Ahmed Bukhsh

“Some Topics in Generalized Convexity” Book Review: This book discusses some of the salient topics in the general convexity domain. It is helpful for students and researchers in the area of optimization, management sciences, operations research and economics. It first talks about some recent developments in the field of generalized convexity. It provides the readers with review of complex analysis, helping them to comprehend the complex area of generalized convexity and variational inequalities.

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