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In this paper, we propose systematic and efficient gradient-based methods for both one-way and two-way partial AUC (pAUC) maximization that are applicable to deep learning. We propose new formulations of pAUC surrogate objectives by using…

Machine Learning · Computer Science 2023-09-19 Dixian Zhu , Gang Li , Bokun Wang , Xiaodong Wu , Tianbao Yang

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Optimization and Control · Mathematics 2015-03-04 Quoc Tran-Dinh , Volkan Cevher

Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article…

Optimization and Control · Mathematics 2010-06-28 Philipp Rostalski , Bernd Sturmfels

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

Optimization and Control · Mathematics 2025-11-07 Venkat Chandrasekaran , Timothy Duff , Jose Israel Rodriguez , Kevin Shu

This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…

Optimization and Control · Mathematics 2025-10-24 V. S. T. Long , B. S. Mordukhovich , N. M. Nam , L. White

We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without…

Optimization and Control · Mathematics 2025-11-26 Chenyang Qiu , Zongli Lin

Recently, unmanned aerial vehicle (UAV) has attracted much attention due to its flexible deployment and controllable mobility. As the general communication network cannot meet the emergency requirements, in this paper we study the multi-UAV…

Information Theory · Computer Science 2024-07-17 Yixin Zhang , Wenchi Cheng

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

Optimization and Control · Mathematics 2020-12-29 Sheheryar Mehmood , Peter Ochs

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…

Optimization and Control · Mathematics 2019-11-28 Darina Dvinskikh , Eduard Gorbunov , Alexander Gasnikov , Pavel Dvurechensky , Cesar A. Uribe

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this…

Optimization and Control · Mathematics 2023-09-06 Dandan Wang , Daokuan Zhu , Kin Cheong Sou , Jie Lu

This paper describes a simple framework for structured sparse recovery based on convex optimization. We show that many structured sparsity models can be naturally represented by linear matrix inequalities on the support of the unknown…

Machine Learning · Computer Science 2015-03-04 Marwa El Halabi , Volkan Cevher

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…

Machine Learning · Computer Science 2021-10-14 Yifei Wang , Mert Pilanci

We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization…

We study the optimal routing problem in decentralized exchanges built on Constant Function Market Makers when trades can be split across multiple heterogeneous pools and execution incurs fixed on-chain costs (gas fees). While prior routing…

Optimization and Control · Mathematics 2026-03-04 Carlos Escudero , Felipe Lara , Miguel Sama

We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…

Optimization and Control · Mathematics 2018-03-14 Nguyen Dinh , Miguel A. Goberna , Marco A. López , Michel Volle

In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-27 Ivano Notarnicola , Mauro Franceschelli , Giuseppe Notarstefano

Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust…

Risk Management · Quantitative Finance 2018-05-21 William B. Haskell , Wenjie Huang , Huifu Xu

The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and…

Econometrics · Economics 2025-10-21 Hung Tran , Tien Mai , Minh Hoang Ha

Collaborative edge computing (CEC) is an emerging paradigm where heterogeneous edge devices collaborate to fulfill computation tasks, such as model training or video processing, by sharing communication and computation resources.…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-27 Jinkun Zhang , Yuezhou Liu , Edmund Yeh

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the…

Optimization and Control · Mathematics 2014-10-20 Madeleine Udell , Karanveer Mohan , David Zeng , Jenny Hong , Steven Diamond , Stephen Boyd