Finding the Integer Efficient Frontier for Quadratic Capital Budgeting Problems

Abstract. A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints.Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve either secondorder conic programming or linear programming relaxations of conic integer programs at the nodes of the branch-and-bound tree.Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming.We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean-variance capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs and, hence, improving their solvability.

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Capital Budgeting Under Capital Rationing: An Analytical Overview of Optimization Models for Government

Khan

2008

International Journal of Public Administration

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Finding the Integer Efficient Frontier for Quadratic Capital Budgeting Problems

Cited by 4 publications

References 5 publications

Optimal hedging under indivisible choices

Optimal hedging under indivisible choices

Conic mixed-integer rounding cuts

Capital Budgeting Under Capital Rationing: An Analytical Overview of Optimization Models for Government

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