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The book covers several new research findings in the area of
generalized convexity and integral inequalities. Integral
inequalities using various type of generalized convex functions are
applicable in many branches of mathematics such as mathematical
analysis, fractional calculus, and discrete fractional calculus.
The book contains integral inequalities of Hermite-Hadamard type,
Hermite- Hadamard-Fejer type and majorization type for the
generalized strongly convex functions. It presents Hermite-Hadamard
type inequalities for functions defined on Time scales. Further, it
provides the generalization and extensions of the concept of
preinvexity for interval-valued functions and stochastic processes,
and give Hermite-Hadamard type and Ostrowski type inequalities for
these functions. These integral inequalities are utilized in
numerous areas for the boundedness of generalized convex functions.
Features: Covers Interval-valued calculus, Time scale calculus,
Stochastic processes – all in one single book Numerous examples
to validate results Provides an overview of the current state of
integral inequalities and convexity for a much wider audience,
including practitioners Applications of some special means of real
numbers are also discussed The book is ideal for anyone teaching or
attending courses in integral inequalities along with researchers
in this area.
Pseudolinear Functions and Optimization is the first book to focus
exclusively on pseudolinear functions, a class of generalized
convex functions. It discusses the properties, characterizations,
and applications of pseudolinear functions in nonlinear
optimization problems. The book describes the characterizations of
solution sets of various optimization problems. It examines
multiobjective pseudolinear, multiobjective fractional
pseudolinear, static minmax pseudolinear, and static minmax
fractional pseudolinear optimization problems and their results.
The authors extend these results to locally Lipschitz functions
using Clarke subdifferentials. They also present optimality and
duality results for h-pseudolinear and semi-infinite pseudolinear
optimization problems. The authors go on to explore the
relationships between vector variational inequalities and vector
optimization problems involving pseudolinear functions. They
present characterizations of solution sets of pseudolinear
optimization problems on Riemannian manifolds as well as results on
pseudolinearity of quadratic fractional functions. The book also
extends n-pseudolinear functions to pseudolinear and n-pseudolinear
fuzzy mappings and characterizations of solution sets of
pseudolinear fuzzy optimization problems and n-pseudolinear fuzzy
optimization problems. The text concludes with some applications of
pseudolinear optimization problems to hospital management and
economics. This book encompasses nearly all the published
literature on the subject along with new results on semi-infinite
nonlinear programming problems. It will be useful to readers from
mathematical programming, industrial engineering, and operations
management.
Pseudolinear Functions and Optimization is the first book to focus
exclusively on pseudolinear functions, a class of generalized
convex functions. It discusses the properties, characterizations,
and applications of pseudolinear functions in nonlinear
optimization problems. The book describes the characterizations of
solution sets of various optimization problems. It examines
multiobjective pseudolinear, multiobjective fractional
pseudolinear, static minmax pseudolinear, and static minmax
fractional pseudolinear optimization problems and their results.
The authors extend these results to locally Lipschitz functions
using Clarke subdifferentials. They also present optimality and
duality results for h-pseudolinear and semi-infinite pseudolinear
optimization problems. The authors go on to explore the
relationships between vector variational inequalities and vector
optimization problems involving pseudolinear functions. They
present characterizations of solution sets of pseudolinear
optimization problems on Riemannian manifolds as well as results on
pseudolinearity of quadratic fractional functions. The book also
extends n-pseudolinear functions to pseudolinear and n-pseudolinear
fuzzy mappings and characterizations of solution sets of
pseudolinear fuzzy optimization problems and n-pseudolinear fuzzy
optimization problems. The text concludes with some applications of
pseudolinear optimization problems to hospital management and
economics. This book encompasses nearly all the published
literature on the subject along with new results on semi-infinite
nonlinear programming problems. It will be useful to readers from
mathematical programming, industrial engineering, and operations
management.
This book is based on the lecture notes of the author delivered to
the students at the Institute of Science, Banaras Hindu University,
India. It covers simplex, revised simplex, two-phase method,
duality, dual simplex, complementary slackness, transportation and
assignment problems with good number of examples, clear proofs,
MATLAB codes and homework problems. The book will be useful for
both students and practitioners.
This book discusses unconstrained optimization with R-a free,
open-source computing environment, which works on several
platforms, including Windows, Linux, and macOS. The book highlights
methods such as the steepest descent method, Newton method,
conjugate direction method, conjugate gradient methods,
quasi-Newton methods, rank one correction formula, DFP method, BFGS
method and their algorithms, convergence analysis, and proofs. Each
method is accompanied by worked examples and R scripts. To help
readers apply these methods in real-world situations, the book
features a set of exercises at the end of each chapter. Primarily
intended for graduate students of applied mathematics, operations
research and statistics, it is also useful for students of
mathematics, engineering, management, economics, and agriculture.
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