Contributed Session Wed.3.MA 042

Wednesday, 15:15 - 16:45 h, Room: MA 042

Cluster 14: Mixed-integer nonlinear programming [...]

Topics in mixed-integer nonlinear programming III


Chair: Duan Li



Wednesday, 15:15 - 15:40 h, Room: MA 042, Talk 1

Duan Li
MIQP solvers for quadratic programs with cardinality and minimum threshold constraints: A semidefinite program approach

Coauthors: Xiaoling Sun, Xiaojin Zheng


We consider in this research the cardinality constrained quadratic programming problem (P) that arise naturally in various real-world applications such as portfolio selection and subset selection in regression. We first investigate how to construct tighter semidefinite program (SDP) relaxation of the problem by applying a special Lagrangian decomposition scheme to the diagonal decomposition of the problem. We show that for any fixed diagonal decomposition, the dual problem can be reduced to a second-order cone program (SOCP), which
is the continuous relaxation of the perspective reformulation of
(P). This leads to an SDP formulation for computing the "best'' diagonal decomposition in the perspective reformulation. Numerical results comparing the performance of different MIQP reformulations of the problem show that the proposed SDP approach can help to improve the performance of the standard MIQP solvers for cardinality constrained quadratic programs.



Wednesday, 15:45 - 16:10 h, Room: MA 042, Talk 2

Vikas Sharma
A duality based approach for a class of bilevel programming problems

Coauthors: Kalpana Dahiya, Vanita Verma


This paper proposes a globally convergent algorithm for a class of bilevel programming problem where the upper level objective function is linear fractional and lower level objective function is linear with an additional restriction on decision variables that are integers for upper level and continuous for lower level. The proposed algorithm makes use of duality theory, to transform the given bilevel problem into a nonlinear programming problem, which can be solved by solving a series of linear fractional programming problems with linear constraints, to obtain a global optimal solution of the original bilevel programming problem. A numerical example is also discussed which illustrates the feasibility and efficiency of the proposed algorithm.


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