相关论文: Facility Leasing with Penalties

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

We present a proximal policy optimization (PPO) agent trained through curriculum learning (CL) principles and meticulous reward engineering to optimize a real-world high-throughput waste sorting facility. Our work addresses the challenge of…

In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…

We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity…

Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case…

We consider Online Facility Location in the framework of learning-augmented online algorithms. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon…

This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…

Classical clustering problems such as \emph{Facility Location} and \emph{$k$-Median} aim to efficiently serve a set of clients from a subset of facilities -- minimizing the total cost of facility openings and client assignments in Facility…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…

Settings such as lending and policing can be modeled by a centralized agent allocating a resource (loans or police officers) amongst several groups, in order to maximize some objective (loans given that are repaid or criminals that are…

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via…

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…

Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing linear programs which model…

This paper focuses on the Facility Location Problem with Bernoulli Demand, a discrete facility location problem with uncertainty where the joint distribution of the customers' demands is expressed by means of a set of possible scenarios. A…

Adversarial examples are a challenging open problem for deep neural networks. We propose in this paper to add a penalization term that forces the decision function to be at in some regions of the input space, such that it becomes, at least…

We reinterpret some online greedy algorithms for a class of nonlinear "load-balancing" problems as solving a mathematical program online. For example, we consider the problem of assigning jobs to (unrelated) machines to minimize the sum of…

We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate…

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…