A cutting- plane approach for semi- infinite mathematical programming

Many situations ranging from industrial to social via economic and environmental problems may be cast into a Semi-infinite mathematical program. In this paper, the cutting-plane approach which lends itself better for standard non-linear programs is exploited with good reasons for grappling with linear, convex and geometric Semi-infinite programs. For each case, computational aspects are discussed and convergence statements established. Simple numerical examples are also provided for the sake of illustration. The paper ends by briefly comparing the cutting-plane approachdiscussed here with other existing approaches and by stressing the necessity of pushing forward a Decision Support System effectively capable for helping someone faced with a problem that can be formulated as a Semi-infinite mathematical program

Combining randomness and fuzziness

Fuzzy random variable (frv) is one of the most successful mathematical tool for taking an intellectual step towards situations where randomness and fuzziness co-occur. This hybrid concept is discussed in this paper along with an outline of its key features. We also list some applications of fuzzy random variables in solving concrete problems and we provide a numerical example showing how randomness and fuzziness can be combined in an optimization setting. The paper ends with some concluding remarks emphasizing perspectives on potential research directions. Keywords: random variable, fuzzy number, fuzzy random variable, optimizationAfrican Journal of Science and Technology Vol. 5(2) 2004: 51-5