相关论文: Introducing the Expohedron for Efficient Pareto-op…
We leverage the connections between nonexpansive maps, monotone Lipschitz operators, and proximal mappings to obtain near-optimal (i.e., optimal up to poly-log factors in terms of iteration complexity) and parameter-free methods for solving…
We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function,…
Fair allocation of indivisible goods studies allocating $m$ goods among $n$ agents in a fair manner. While fairness is a fundamental requirement in many real-world applications, it often conflicts with (economic) efficiency. This raises a…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm…
The problem of approximating the Pareto front of a multiobjective optimization problem can be reformulated as the problem of finding a set that maximizes the hypervolume indicator. This paper establishes the analytical expression of the…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
In this paper, we consider black-box multiobjective optimization problems in which all objective functions are not given analytically. In multiobjective optimization, it is important to produce a set of uniformly distributed discrete…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning…
This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…
We study the fair division of indivisible items. In the general model, the goal is to allocate $m$ indivisible items to $n$ agents while satisfying fairness criteria such as MMS, EF1, and EFX. We also study a recently-introduced graphical…
We consider the problem of generating rankings that are fair towards both users and item producers in recommender systems. We address both usual recommendation (e.g., of music or movies) and reciprocal recommendation (e.g., dating).…
The Birkhoff polytope (the convex hull of the set of permutation matrices) is frequently invoked in formulating relaxations of optimization problems over permutations. The Birkhoff polytope is represented using $\Theta(n^2)$ variables and…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
Ranking plays a central role in connecting users and providers in Information Retrieval (IR) systems, making provider-side fairness an important challenge. While recent research has begun to address fairness in ranking, most existing…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
We present a comprehensive framework that unifies several research areas within the context of vertex-weighted bipartite graphs, providing deeper insights and improved solutions. The fundamental solution concept for each problem involves…
The Assignment problem is a fundamental and well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, a group of agents expresses preferences over a set of items,…
The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then…