Related papers: BilevelJuMP.jl: Modeling and Solving Bilevel Optim…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
Julia is a new language for writing data analysis programs that are easy to implement and run at high performance. Similarly, the Dynamic Distributed Dimensional Data Model (D4M) aims to clarify data analysis operations while retaining…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the…
Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
This paper proposes integrating Aspect-oriented Programming (AOP) into Julia, a language widely used in scientific and High-Performance Computing (HPC). AOP enhances software modularity by encapsulating cross-cutting concerns, such as…
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…
InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging…
This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most…
We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…
This chapter presents the Bilevel Optimization LIBrary of the test problems (BOLIB for short), which contains a collection of test problems, with continuous variables, to help support the development of numerical solvers for bilevel…
Compilers are indispensable for transforming code written in high-level languages into performant machine code, but their general-purpose optimizations sometimes fall short. Domain experts might be aware of certain optimizations that the…
Marginal effects analysis is fundamental to interpreting statistical models, yet existing implementations face computational constraints that limit analysis at scale. We introduce two Julia packages that address this gap. Margins.jl…
We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally…