#optimality conditions

Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49975 DOI: 10.4236/ajor.2014.45031 Author(s) I. Husain1, A. Ahmed2, Abdul Raoof Shah2 ABSTRACT A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.eww140929gjr KEYWORDS Control Problem, Support Function, Optimality Conditions, Generalized Convexity, Wolfe Type Duality, Nonlinear Programming Problem

Conical Approach to Linear Programming The conical approach provides a geometrical understanding of optimization and is a powerful research tool and useful problem-solving technique (for example, in decision support and real time control applications). Conical optimality conditions are first stated in a very general optimization framework, and then applied to linear programming. A complete theory along with primal and dual algorithms is given, and solutions and algorithms are also provided for vector and robust linear optimization. The advantages of parameter dependence of conical methods are fully discussed. In addition to numerical results, the book provides source codes and detailed documentation of a Modula-2 implementation for the main algorithms.