Related papers: Constrained Assortment and Price Optimization unde…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
Computing the exact optimal experimental design has been a longstanding challenge in various scientific fields. This problem, when formulated using a specific information function, becomes a mixed-integer nonlinear programming (MINLP)…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper studies an online selection problem, where a seller seeks to sequentially sell multiple copies of an item to arriving buyers. We consider an adversarial setting, making no modeling assumptions about buyers' valuations for the…
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning…
We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing…
We focus on designing combinatorial algorithms for the Capacitated Network Design problem (Cap-SNDP). The Cap-SNDP is the problem of satisfying connectivity requirements when edges have costs and hard capacities. We begin by showing that…
This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati et al. (2017) under the…
This paper investigates the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through an $\ell_0$ cardinality constraint. While branch-and-bound (BnB) frameworks can certify optimality…
This paper investigates the performance, in terms of choice probabilities and correlations, of existing and new specifications of closed-form route choice models with flexible correlation patterns, namely the Link Nested Logit (LNL), the…
We study the competitive facility location problem, where a firm aims to establish new facilities in a market already occupied by competitors. In this problem, customer behavior is crucial for making optimal location decisions. We explore a…
A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…
Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice…
The gradient descent (GD) method has been used widely to solve parameter estimation in generalized linear models (GLMs), a generalization of linear models when the link function can be non-linear. In GLMs with a polynomial link function, it…
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
The network pricing problem (NPP) is a bilevel problem, where the leader optimizes its revenue by deciding on the prices of certain arcs in a graph, while expecting the followers (also known as the commodities) to choose a shortest path…
Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we…