arXiv subjects

Adrian Göß

Publications and source records attributed to Adrian Göß.

6 recordsLinked to original sources

arXiv2026

Complexity of Integer Programming in Reverse Convex Sets via Boundary Hyperplane Cover

We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the case of bounded reverse convex constraints with a polyhedral domain. We introduce a structure, \emph{Boundary Hyperplane Cover}, that permits this problem to be solved in polynomial time in fixed dimension provided the number of nonlinear reverse convex sets is fixed.

math.OC↗

arXiv2026

iPack: Intuitive Bin Packing with Large Language Models

Robotics and automation are increasingly influential in logistics but remain largely confined to traditional warehouses. In grocery retail, advancements such as cashier-less supermarkets exist, yet customers still manually pick and pack groceries. While there has been a substantial focus in robotics on the bin picking problem, the task of packing objects and groceries has remained largely untouched. However, packing grocery items in the right order is crucial for preventing product damage, e.g., heavy objects should not be placed on top of fragile ones. However, the exact criteria for the right packing order are hard to define, in particular given the huge variety of objects typically found in stores. In this paper, we introduce LLM-Pack, a novel approach for grocery packing. LLM-Pack leverages language and vision foundation models for identifying groceries and generating a packing sequence that mimics human packing strategy. LLM-Pack does not require dedicated training to handle new grocery items and its modularity allows easy upgrades of the underlying foundation models. We extensively evaluate our approach to demonstrate its performance. We will make the source code of LLMPack publicly available upon the publication of this manuscript.

cs.RO↗

arXiv2026

Clash of MINLP Relaxations: Piecewise Linear vs. Global Parabolic

Solving mixed-integer nonlinear programs (MINLPs) typically relies on constructing relaxations that are easier to tackle than the original problem. Recently, global parabolic (PARA) relaxations were introduced, featuring separable quadratic functions -- paraboloids -- as global under- or overestimators of general nonlinear constraint functions. So far, the paraboloids are all computed at once by solving a mixed-integer linear program (MIP). For small tolerances or wide function domains, the corresponding MIP grows in size and is eventually intractable, reventing a meaningful comparison with established relaxation techniques. We therefore propose a novel iterative method to compute PARA approximations that succeeds on all tolerance-domain combinations where the original one has failed. The computational study is preceded by a thorough theoretical explanation and analysis. Finally, the improved method enables a computational comparison with piecewise linear (PWL) relaxations in terms of runtime on general MINLP instances. The results show that the modern solver SCIP can solve PWL relaxations faster when the tolerance is high, shifting strongly in favor of PARA for tighter tolerances. We attribute the effect to the difference in the corresponding problem size: PWL relaxations introduce binary variables to identify the active linear piece and their number grows with decreasing tolerance. PARA, on the other hand, does not require additional variables such that the dimension is maintained. For problems with at least one (co)sine constraint, the effect significantly amplifies. Thereby, for medium tolerances, PARA relaxations outperform SCIP stand-alone. Applied problems like alternating current optimal power flow (AC-OPF) feature such constraint types, leaving PARA a viable relaxation strategy.

math.OC↗

arXiv2025

The SCIP Optimization Suite 10.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 10.0. The updates in SCIP 10.0 include a new solving mode for exactly solving rational mixed-integer linear programs, a new presolver for detecting implied integral variables, a novel cut-based conflict analysis and separator for flower inequalities, two new heuristics, a novel tool for explaining infeasibility, a new interface for nonlinear solvers as well as improvements in symmetry handling, branching strategies, and SCIP's Benders' decomposition framework. SCIP Optimization Suite 10.0 also includes new and improved features in the the presolving library PaPILO, the parallel framework UG, and the decomposition framework GCG. Moreover, the SCIP Optimization Suite 10.0 contains MIP-DD, the first open-source delta debugger for mixed-integer programming solvers. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.

math.OC↗

arXiv2025

Norm-induced Cuts: Outer Approximation for Lipschitzian Constraint Functions

In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz constant. In recent literature, methods based on non-convex outer approximation are proposed for tackling one-dimensional equality constraints that are Lipschitz with respect to the maximum norm. To the best of our knowledge, however, there does not exist a non-convex outer approximation method for a general problem class. We introduce a meta-level solution framework to solve such problems and tackle the underlying theoretical foundations. Considering the feasible domain without the constraint function as manageable, our method relaxes the multidimensional constraint and iteratively refines the feasible region by means of norm-induced cuts, relying on an oracle for the resulting subproblems. We show the method's correctness and investigate the problem complexity. In order to account for discussions about functionality, limits, and extensions, we present computational examples including illustrations.

math.OC↗

arXiv2025

Parabolic Approximation & Relaxation for MINLP

We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means of paraboloids, which are polynomials of degree two with univariate quadratic terms, and relies on a Lipschitz property only. These approximations are then integrated into the original problem. To this end, we introduce a novel approach to compute globally valid epigraph approximations by paraboloids via a Mixed-Integer Linear Programming (MIP) model. We emphasize the possibility of performing such approximations a-priori and providing them in form of a lookup table, and then present several ways of leveraging the approximations to tackle the original problem. We provide the necessary theoretical background and conduct computational experiments on instances of the MINLPLib. As a result, this approach significantly accelerates the solution process of MINLP problems, particularly those involving many trigonometric or few exponential functions. In general, we highlight that the proposed technique is able to exploit advances in Mixed-Integer Quadratically-Constrained Programming (MIQCP) to solve MINLP problems.

math.OC↗