Sphere Methods for LP

  • Katta G. Murty
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 137)


For solving an optimization problem in which an objective function z(x) is to be minimized subject to constraints, starting with an initial feasible solution, a method that works by generating a sequence of feasible solutions along which the objective value z(x) strictly decreases is known as a descent algorithm. Strict improvement in the objective value in each step is an appealing property, and hence descent algorithms are the most sought after.

If the original objective function is to be maximized instead, algorithms that maintain feasibility and improve the objective value (i.e., here, increasing its value) in every step are also referred to as descent algorithms.


Feasible Solution Step Length Line Search Objective Plane Ball Center 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Systems Engineering DepartmentKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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