Mixed integer programming with a class of nonlinear convex constraints
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 th...
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| Published in: | Discrete optimization Vol. 24; pp. 66 - 86 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.05.2017
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| ISSN: | 1572-5286, 1873-636X |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Vinel, Alexander Krokhmal, Pavlo A. |
| Author_xml | – sequence: 1 givenname: Alexander orcidid: 0000-0003-3095-5986 surname: Vinel fullname: Vinel, Alexander email: alexander.vinel@auburn.edu organization: Department of Industrial and Systems Engineering, Auburn University, 3301 Shelby Center, Auburn, AL 36849, USA – sequence: 2 givenname: Pavlo A. surname: Krokhmal fullname: Krokhmal, Pavlo A. organization: Department of Systems & Industrial Engineering, University of Arizona, 1127 E James E. Rogers Way, Tucson, AZ 85721, USA |
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| Keywords | Measures of risk Valid inequalities Mixed-integer nonlinear programming Conic programming Quasi-arithmetic average |
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