Invited Session Tue.1.MA 005

Tuesday, 10:30 - 12:00 h, Room: MA 005

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

Efficient solvers for mixed integer nonlinear optimization problems


Chair: Leo Liberti and Pietro Belotti



Tuesday, 10:30 - 10:55 h, Room: MA 005, Talk 1

Stefan Vigerske
Solving MINLPs with SCIP


We discuss recent extensions of the constraint integer programming
framework SCIP for solving mixed-integer nonlinear programs. Nonlinear
constraints (convex or nonconvex) are handled within an LP-based
branch-and-cut algorithm by reformulation, linear relaxation,
and domain propagation. In an extensive computational study, we compare
the performance of our implementation with state-of-the-art
solvers for MINLP and analyze the impact of various solver components
on the overall performance.



Tuesday, 11:00 - 11:25 h, Room: MA 005, Talk 2

Pietro Belotti
Separation of valid inequalities for multilinear functions


We develop efficient methods to separate valid inequalities for a set defined by a multlinear function, i.e., a function that is linear when all variables but one are fixed. One method takes advantage of a tensor representation of a multilinear term, while the other uses a divide-and-conquer technique coupled with dynamic programming in order to find the most violated inequality. Some preliminary experimental results are reported.



Tuesday, 11:30 - 11:55 h, Room: MA 005, Talk 3

Hongbo Dong
On box constrained quadratic programming with binary indicators


We consider (nonconvex) quadratic programming with box constraints and binary variables that are the "on/off'' switches for continuous variables. We prove some geometric results on the corresponding convex hull, and show how to lift a class of valid inequalities for Box QP to include binary indicators. We prove that the separation problem for these lifted cuts is polynomially solvable, as long as the number of binary variables included are not too many. Finally computational results will be reported to verify the effectiveness of these cuts.


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