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Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent…
The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are…
First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional…
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
We consider the problem of static assortment optimization, where the goal is to find the assortment of size at most $C$ that maximizes revenues. This is a fundamental decision problem in the area of Operations Management. It has been shown…
How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a…
Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an…
In the resource allocation problem (RAP), the goal is to divide a given amount of resource over a set of activities while minimizing the cost of this allocation and possibly satisfying constraints on allocations to subsets of the…
We define a natural class of range query problems, and prove that all problems within this class have the same time complexity (up to polylogarithmic factors). The equivalence is very general, and even applies to online algorithms. This…
Algorithmic reasoning -- the ability to perform step-by-step logical inference -- has become a core benchmark for evaluating reasoning in graph neural networks (GNNs) and large language models (LLMs). Ideally, one would like to design a…
We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of…