Approximation methods for non-convex curves

Article Abstract:

Two algorithms were created to calculate non-convex curve's upper and lower approximate curves. The algorithms initially entails mapping of non-convex curve into a convex curve with the use of p-power transformation. The inverse of the p-power transformation is taken to allow mapping of the approximate curves into the original space. Such algorithms can be utilized to approximate the non-convex efficient frontiers of bicriteria optimization problems.

Operations Research, Research, Numerical analysis, Mathematical optimization, Optimization theory, Mathematical programming

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The gap function of a convex multicriteria optimization problem

Article Abstract:

A generalization of the gap function defined for a convex optimization problem and an analysis of its properties shows that the functions may provide insights into the traffic equilibrium principle. The gap functions for the convex optimization problem and convex multicriteria optimization problem may also be generalizable to abstract spaces such as Banach space or Hausdorff space.

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Optimum component test plans for systems with dependent components

Article Abstract:

A model for managing the testing of dependent components is developed and evaluated. The model assumes the stochastic dependence as a result of the same working environment and uses a hybrid of the cutting-plane idea and the column generation technique. The approach is the first attempt to measure component testing variables where the components are stochastically dependent.

Principal components analysis

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