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The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version…

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…

We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…

Developing automatic Math Word Problem (MWP) solvers has been an interest of NLP researchers since the 1960s. Over the last few years, there are a growing number of datasets and deep learning-based methods proposed for effectively solving…

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…

The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…

Multi-objective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multi-objective optimization problems. In fact, many real-world multi-objective problems…

We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the…

This paper introduces ItsOPT, an inexact two-level smoothing optimization framework designed to find first-order critical points of nonsmooth and nonconvex functions. The framework involves two levels of methodologies: at the upper level, a…

Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…

Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes…

A class of smoothing methods is proposed for solving mathematical programs with equimibrium constraints. We introduce new and very simple regularizations of the complementarity constraints. Some estimate distance to optimal solution and…

This paper presents a new fast active-set quadratic programming (QP) solver based on inverse matrix updates, which is suitable for real-time model predictive control (MPC). This QP solver, called imuQP (inverse matrix update QP), is based…

Based on smoothing techniques, we propose two new methods to solve linear complementarity problems (LCP) called TLCP and Soft-Max. The idea of these two new methods takes inspiration from interior-point methods in optimization. The…

In this paper we present GridapTopOpt, an extendable framework for level set-based topology optimisation that can be readily distributed across a personal computer or high-performance computing cluster. The package is written in Julia and…

We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to…

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…

We propose a new disjunctive regularization for mathematical programs with complementarity constraints (MPCC). Its feasible set coincides with that of the Kanzow-Schwartz regularization. However, their functional descriptions differ…

In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…