Nonlinear Programming: Theory and Algorithms

Nonlinear Programming: Theory and Algorithms—now inan extensively updated Third Edition—addresses the problem ofoptimizing an objective function in the presence of equality andinequality constraints. Many realistic problems cannot beadequately represented as a linear program owing to the nature ofthe nonlinearity of the objective function and/or the nonlinearityof any constraints. The Third Edition begins with a generalintroduction to nonlinear programming with illustrative examplesand guidelines for model construction.

Concentration on the three major parts of nonlinear programmingis provided:

• Convex analysis with discussion of topological properties ofconvex sets, separation and support of convex sets, polyhedralsets, extreme points and extreme directions of polyhedral sets, andlinear programming
• Optimality conditions and duality with coverage of the nature,interpretation, and value of the classical Fritz John (FJ) and theKarush-Kuhn-Tucker (KKT) optimality conditions; theinterrelationships between various proposed constraintqualifications; and Lagrangian duality and saddle point optimalityconditions
• Algorithms and their convergence, with a presentation ofalgorithms for solving both unconstrained and constrained nonlinearprogramming problems

Important features of the Third Edition include:

• New topics such as second interior point methods, nonconvexoptimization, nondifferentiable optimization, and more
• Updated discussion and new applications in each chapter
• Detailed numerical examples and graphical illustrations
• Essential coverage of modeling and formulating nonlinearprograms
• Simple numerical problems
• Advanced theoretical exercises

The book is a solid reference for professionals as well as auseful text for students in the fields of operations research,management science, industrial engineering, applied mathematics,and also in engineering disciplines that deal with analyticaloptimization techniques. The logical and self-contained formatuniquely covers nonlinear programming techniques with a great depthof information and an abundance of valuable examples andillustrations that showcase the most current advances in nonlinearproblems.