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Continuous Optimization

Current Trends and Modern Applications

  • Book
  • © 2005

Overview

Editors:
  1. Vaithilingam Jeyakumar

    1. University of New South Wales, Sydney, Australia

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    You can also search for this editor in PubMed   Google Scholar

  2. Alexander Rubinov

    1. University of Ballarat, Ballarat, Australia

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    You can also search for this editor in PubMed   Google Scholar

  • A research contributed volume presenting substantive survey articles in a number of important topic areas of continuous optimization
  • Contains timely research articles in optimization theory, and numerical optimization including optimization software and applications in different fields such as data analysis and scattering problems

Part of the book series: Applied Optimization (APOP, volume 99)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Surveys

    1. Front Matter

      Pages 1-1
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    2. Linear Semi-infinite Optimization: Recent Advances

      • Miguel A. Goberna
      Pages 3-22

    3. Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolation

      • Hou-Duo Qi
      Pages 23-49

    4. Optimization Methods in Direct and Inverse Scattering

      • Alexander G. Ramm, Semion Gutman
      Pages 51-110

    5. On Complexity of Stochastic Programming Problems

      • Alexander Shapiro, Arkadi Nemirovski
      Pages 111-146

    6. Nonlinear Optimization in Modeling Environments

      • János D. Pintér
      Pages 147-173

    7. Supervised Data Classification via Max-min Separability

      • Adil M. Bagirov, Julien Ugon
      Pages 175-207

    8. A Review of Applications of the Cutting Angle Methods

      • Gleb Beliakov
      Pages 209-248

  3. Theory and Numerical Methods

    1. Front Matter

      Pages 249-249
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    2. A Numerical Method for Concave Programming Problems

      • Altannar Chinchuluun, Enkhbat Rentsen, Panos M. Pardalos
      Pages 251-273

    3. Convexification and Monotone Optimization

      • Xiaoling Sun, Jianling Li, Duan Li
      Pages 275-291

    4. Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs

      • Nguyen Dinh, Gue Myung Lee, Anh Le Tuan
      Pages 293-319

    5. Slice Convergence of Sums of Convex functions in Banach Spaces and Saddle Point Convergence

      • Robert Wenczel, Andrew Eberhard
      Pages 321-341

    6. Topical Functions and their Properties in a Class of Ordered Banach Spaces

      • Hossein Mohebi
      Pages 343-361

  4. Applications

    1. Front Matter

      Pages 363-363
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    2. Dynamical Systems Described by Relational Elasticities with Applications

      • Musa Mammadov, Alexander Rubinov, John Yearwood
      Pages 365-385

    3. Impulsive Control of a Sequence of Rumour Processes

      • Charles Pearce, Yalcin Kaya, Selma Belen
      Pages 387-407

    4. Minimization of the Sum of Minima of Convex Functions and Its Application to Clustering

      • Alexander Rubinov, Nadejda Soukhoroukova, Julien Ugon
      Pages 409-434

    5. Analysis of a Practical Control Policy for Water Storage in Two Connected Dams

      • Phil Howlett, Julia Piantadosi, Charles Pearce
      Pages 435-450
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Keywords

About this book

Continuous optimization is the study of problems in which we wish to opti­ mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza­ tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re­ search in continuous optimization has produced a variety of theoretical devel­ opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin­ uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.

Editors and Affiliations

  • University of New South Wales, Sydney, Australia

    Vaithilingam Jeyakumar

  • University of Ballarat, Ballarat, Australia

    Alexander Rubinov

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