Optimierung über gemischt-ganzzahligen Polynomprogramme

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This research project is devoted to the study of algorithms for optimizing over mixed integer poloynomial programs. Mixed integer polynomial programs are a significant generalization of linear integer programs in the sense that the constraints of a polynomial program are polynomial inequalities or equations in the variables. The algorithms to be designed will be based on generalizations of various results from the theory of linear integer programming and will try to follow the basic algorithmic streamline in integer programming. More precisely, we plan to develop some basic theory for designing dual type methods, primal type methods, and finally a primal dual method for mixed integer polynomial programs. As a result we expect various theoretical results about the structure of the set of feasible solutions that will be used in our algorithms. We intend to test these algorithmic ideas on polynomial systems arising from questions in chemical engineering that are investigated in the research projects TP3, TP4 and TP5. Indeed these applications motivate this project.