A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution another problem. As consequence, bilevel able model hierarchical decision processes. This appealing for modeling real-world problems, but it also makes resulting models hard solve theory and practice. The scientific interest computational increased lot over last decade still growing. Independent whether problem itself contains integer or not, many state-of-the-art approaches make use techniques that originate from mixed-integer programming. These include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, problem-specific decomposition methods. In this survey article, we review bilevel-tailored exploit these problems. To end, first consider problems with convex or, particular, linear lower-level discussed methods stem original works 1980’s but, on other hand, actively researched today. Second, modern algorithmic contain integrality constraints lower level. Moreover, briefly discuss area nonlinear Third, devote attention more specific fields such as pricing interdiction genuinely bilinear thus nonconvex aspects. Finally, sketch list open questions areas optimization, may lead interesting future research will further propel fascinating active research.