Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions.
['Andreas H. Hamel', 'Andreas Löhne', 'Birgit Rudloff']
I am writing a research paper on a idea Benson type algorithms for linear vector optimization and applications
[{"from": "human", "value": "I am writing a research paper on a idea Benson type algorithms for linear vector optimization and applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions."}]