Alpcan, TansuEveritt, TomHutter, Marcus2015-08-122015-08-12978-1-4799-5999-01662-9019http://hdl.handle.net/1885/14703an we measure the difficulty of an optimization problem? Although optimization plays a crucial role in modern science and technology, a formal framework that puts problems and solution algorithms into a broader context has not been established. This paper presents a conceptual approach which gives a positive answer to the question for a broad class of optimization problems. Adopting an information and computational perspective, the proposed framework builds upon Shannon and algorithmic information theories. As a starting point, a concrete model and definition of optimization problems is provided. Then, a formal definition of optimization difficulty is introduced which builds upon algorithmic information theory. Following an initial analysis, lower and upper bounds on optimization difficulty are established. One of the upper-bounds is closely related to Shannon information theory and black-box optimization. Finally, various computational issues and future research directions are discussed.© 2014 IEEE2014-1110.1109/ITW.2014.6970853