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Copositive (Cop) and Completely Positive (ComP) Optimization is a recent and growing area of research. It has shown that several NP-hard optimization problems can be expressed as Cop or Comp programs, linear programs over the convex cone of copositive or completely positive matrices.
In this seminar, properties of copositive/completely positive matrices, algorithms for copositive detection and conic reformulation of some difficult optimization problems are reviewed. The importance of these reformulations to obtain tight relaxations is also discussed. Applications related to fractional quadratic problems and the repair of infeasible systems are also presented. [Paula Amaral is an auxiliary professor at the Department of Mathematics and member of CMA at Universidade Nova de Lisboa. Her research area is related to copositive optimization, fractional problems, infeasibility analysis and timetabling problems.]
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