Mixed integer programming with a class of nonlinear convex constraints

作者：Vinel Alexander^*; Krokhmal Pavlo A

来源：Discrete Optimization, 2017, 24: 66-86.

DOI：10.1016/j.disopt.2016.07.002

• Mixed-integer nonlinear programming
• Measures of risk
• Quasi-arithmetic average
• Valid inequalities
• Conic programming

We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be generalized to the problems under consideration. Particularly, we consider a branch-and-bound method based on outer polyhedral approximations, lifted nonlinear cuts, and linear disjunctive cuts. Results of numerical experiments with discrete portfolio optimization models are presented.

• 出版日期2017-5