Continuous Optimization

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

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.

• Newton's method
• analysis
• linear optimization
• model
• modeling
• nonlinear optimization
• numerical methods
• optimization
• programming

• University of New South Wales, Sydney, Australia

  Vaithilingam Jeyakumar

• University of Ballarat, Ballarat, Australia

  Alexander Rubinov

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