6533b835fe1ef96bd129f2ba
RESEARCH PRODUCT
Strict quasi-concavity and the differential barrier property of gauges in linear programming
Abdessamad Barbarasubject
Control and OptimizationLinear programmingSimple (abstract algebra)Applied MathematicsMathematical analysisDifferentiable functionManagement Science and Operations ResearchDifferential (infinitesimal)Gauge (firearms)Representation (mathematics)Interior point methodOrthantMathematicsdescription
Concave gauge functions were introduced to give an analytical representation of cones. In particular, they give a simple and a practical representation of the positive orthant. There is a wide choice of concave gauge functions with interesting properties, representing the same cone. Besides the fact that a concave gauge cannot be identically zero on a cone(), it may be continuous, differentiable and even on its interior. The purpose of the present paper is to present another approach to penalizing the positivity constraints of a linear programme using an arbitrary strictly quasi-concave gauge representation. Throughout the paper, we generalize the concept of the central path and the analytic centre in terms of these gauges, introduce the differential barrier concept and establish its relationship with strict quasi-concavity.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-11-28 | Optimization |