A Conical Approach to Linear Programming: Scalar and Vector Optimization Problems

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.