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COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDEDNonlinear Programming: Theory and Algorithms--now in an extensively updated Third Edition-- addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programmingOptimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditionsAlgorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problemsImportant features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapterDetailed numerical examples and graphical illustrationsEssential coverage of modeling and formulating nonlinear programsSimple numerical problemsAdvanced theoretical exercisesThe book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
List of contents
CONVEX ANALYSIS.
Convex Sets.
Convex Functions and Generalizations.
OPTIMALITY CONDITIONS AND DUALITY.
The Fritz John and the Karush-Kuhn-Tucker Optimality Conditions.
Constraint Qualifications.
Lagrangian Duality and Saddle Point Optimality Conditions.
ALGORITHMS AND THEIR CONVERGENCE.
The Concept of an Algorithm.
Unconstrained Optimization.
Penalty and Barrier Functions.
Methods of Feasible Directions.
Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming.
Appendices.
Bibliography.
Index.
About the author
Mokhtar S. BAZARAA, PhD, is a Professor at the Georgia Institute of Technology.
HANIF D. SHERALI, PhD, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at Virginia Polytechnic Institute and State University.
C. M. SHETTY, PhD, is a Professor Emeritus at the Georgia Institute of Technology.
Professors Bazaraa and Sherali are also coauthors of the complementary bestselling book,
Linear Programming and Network Flows, Third Edition, also published by Wiley.
Summary
Presenting recent developments of key topics in nonlinear programming, this text looks specifically at three main areas; convex analysis, optimality conditions and dual computational techniques.
