Related papers: optipoly: A Python package for boxed-constrained m…
Given a set $P$ of $n$ planar points, two axes and a real-valued score function $f()$ on subsets of $P$, the Optimal Planar Box problem consists in finding a box (i.e. axis-aligned rectangle) $H$ maximizing $f(H\cap P)$. We consider the…
Compound AI applications, which compose calls to ML models using a general-purpose programming language like Python, are widely used for a variety of user-facing tasks, from software engineering to enterprise automation, making their…
OGRePy is a modern, open-source Python package designed to perform symbolic tensor calculations, with a particular focus on applications in general relativity. Built on an object-oriented architecture, OGRePy encapsulates tensors, metrics,…
Convexification is a core technique in global polynomial optimization. Currently, there are two main approaches competing in theory and practice: the approach of nonlinear programming and the approach based on positivity certificates from…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
QMKPy provides a Python framework for modeling and solving the quadratic multiple knapsack problem (QMKP). It is primarily aimed at researchers who develop new solution algorithms for the QMKP. QMKPy therefore mostly functions as a testbed…
Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit…
PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs). In particular, the package can handle systems with contacts that are described…
In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…
We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
This document introduces a set of 24 box-constrained numerical global optimization problem instances, systematically constructed using the Generalized Numerical Benchmark Generator (GNBG). These instances cover a broad spectrum of problem…
The desirability-function approach is a widely adopted method for optimizing multiple-response processes. Kuhn (2016) implemented the packages desirability and desirability2 in the statistical programming language R, but no comparable…
Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
An important benefit of multi-objective search is that it maintains a diverse population of candidates, which helps in deceptive problems in particular. Not all diversity is useful, however: candidates that optimize only one objective while…
PHCpack is a large software package for solving systems of polynomial equations. The executable phc is menu driven and file oriented. This paper describes the development of phcpy, a Python interface to PHCpack. Instead of navigating…
A novel Python framework for Bayesian optimization known as GPflowOpt is introduced. The package is based on the popular GPflow library for Gaussian processes, leveraging the benefits of TensorFlow including automatic differentiation,…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…