## Invited Session Wed.2.MA 041

#### Wednesday, 13:15 - 14:45 h, Room: MA 041

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

### Structured MINLP and applications

**Chair: Noam Goldberg**

**Wednesday, 13:15 - 13:40 h, Room: MA 041, Talk 1**

**Toni Lastusilta**

Chromatographic separation using GAMS extrinsic functions

**Coauthors: Michael R. Bussieck, Stefan Emet**

**Abstract:**

In chemical and pharmaceutical industries the problem of separating products of a multicomponent mixture can arise. The objective is to efficiently separate the mixture within reasonable costs during a cyclic operation. To optimize the process a boundary value problem that includes differential equations needs to be solved. The presented Mixed-Integer NonLinear Programming (MINLP) model solves an instance of the chromatographic separation process in GAMS by using extrinsic functions. The function library facility that was recently introduced in GAMS 23.7 provides a convenient way of modeling it. The problem has been earlier studied in "Comparisons of solving a chromatographic separation problem using MINLP methods'' by Stefan Emet and Tapio Westerlund.

**Wednesday, 13:45 - 14:10 h, Room: MA 041, Talk 2**

**Noam Goldberg**

Cover inequalities for nearly monotone quadratic MINLPs

**Coauthors: Sven Leyffer, Ilya Safro**

**Abstract:**

Cover Inequalities for nearly monotone quadratic MINLPs

We consider MINLPs arising from novel network optimization formulations with a quadratic objective and constraints that satisfy relaxed monotonicity conditions. We derive valid cover inequalities for these formulations and their linearized counterparts. We study heuristics for generating effective cuts in practice and also consider approximate separation in some cases.

**Wednesday, 14:15 - 14:40 h, Room: MA 041, Talk 3**

**Susan Margulies**

Hilbert's Nullstellensatz and the partition problem: An infeasibility algorithm via the partition matrix and the partition polynomial

**Coauthor: Shmuel Onn**

**Abstract:**

Given a set of integers *W*, the partition problem determines whether or not *W* can be partitioned into two disjoint sets with equal sums. In this talk, we model the partition problem as a system of polynomial equations, and then investigate the complexity of the Hilbert's Nullstellensatz refutations, or certificates of infeasibility, when the underlying set of integers *W* is non-partitionable. We present an algorithm for finding lower bounds on the degree of Hilbert Nullstellensatz refutations, and survey a known result on the complexity of independent set Nullstellensatz certificates. We then describe a method for extracting a square matrix from the combination of Hilbert's Nullstellensatz and the partition problem, and demonstrate that the determinant of that matrix is a polynomial that factors into an iteration of all possible partitions of *W*.