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The book provides an overview of the research in interior point methods since the publication of N. Karmarkar's seminal paper in 1984. Leading international experts have contributed to the book with summaries of their relevant areas of specialization. Part I gives an overview of basic variants of interior point algorithms for linear programming. Duality-theory for LP and sensitivity analysis is developed. Results on the affine scale, path following, potential reduction, infeasible interior point methods and implementation strategies are discussed. Part II deals with nonlinear programming. Here necessary smoothness conditions are introduced and illustrated. Algorithms for general smooth convex problems, complementarity and semidefinite optimization problems are presented. The implementation of barrier methods for general nonlinear optimization problems is also considered. Part III covers some application areas such as combinatorial optimization, global optimization and VLSI design.

Programming (Mathematics) --- Algorithms. --- Programmation (Mathématiques) --- Algorithmes --- Linear Programming --- Programmation (Mathématiques)

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This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

Mathematics. --- Operations research. --- Management science. --- Mathematical optimization. --- Operations Research, Management Science. --- Continuous Optimization. --- Discrete Optimization. --- Mathematical optimization --- Mathematical models --- Models, Mathematical --- Simulation methods --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory

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This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Planning (firm) --- discrete wiskunde --- mathematische modellen --- econometrie --- operationeel onderzoek --- optimalisatie

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Engineering sciences. Technology --- Planning (firm) --- Computer. Automation --- automatisering --- mathematische modellen --- ingenieurswetenschappen

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This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on July 30-August 1, 2012. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

Mathematical models. --- Mathematical optimization. --- Mechanics -- Mathematics. --- Mathematics --- Operations research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematics. --- Operations research. --- Operational analysis --- Operational research --- Math --- Decision making. --- Applied mathematics. --- Engineering mathematics. --- Continuous Optimization. --- Discrete Optimization. --- Operation Research/Decision Theory. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Industrial engineering --- Management science --- Research --- System theory --- Science --- Operations Research/Decision Theory. --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- System analysis --- Decision making --- Mathematical optimization --- Mathematical models