Arvind Raghunathan

NeurIPS Conference 2025 Conference Paper

Constrained Optimization From a Control Perspective via Feedback Linearization

• Runyu Zhang
• Arvind Raghunathan
• Jeff Shamma
• Na Li

Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization—a well-established nonlinear control technique—to solve constrained optimization problems. For equality-constrained optimization, we establish global convergence rates to first-order Karush-Kuhn-Tucker (KKT) points and uncover the close connection between the FL method and the Sequential Quadratic Programming (SQP) algorithm. Building on this relationship, we extend the FL approach to handle inequality-constrained problems. Furthermore, we introduce a momentum-accelerated feedback linearization algorithm and provide a rigorous convergence guarantee.

STOC Conference 1993 Conference Paper

On-line algorithms for cache sharing

• Marshall W. Bern
• Daniel H. Greene
• Arvind Raghunathan

FOCS Conference 1991 Conference Paper

On-line Scheduling in the Presence of Overload

• Sanjoy K. Baruah
• Gilad Koren
• Bhubaneswar Mishra
• Arvind Raghunathan
• Louis E. Rosier
• Dennis E. Shasha

The preemptive scheduling of sporadic tasks on a uniprocessor is considered. A task may arrive at any time, and is characterized by a value that reflects its importance, an execution time that is the amount of processor time needed to completely execute the task, and a deadline by which the task is to complete execution. The goal is to maximize the sum of the values of the completed tasks. An online scheduling algorithm that achieves optimal performance when the system is underloaded and provides a nontrivial performance guarantee when the system is overloaded is designed. The algorithm is implemented using simple data structures to run at a cost of O(log n) time per task, where n bounds the number of tasks in the system at any instant. Upper bounds on the best performance guarantee obtainable by an online algorithm in a variety of settings are derived. >

FOCS Conference 1990 Conference Paper

Online Algorithms for Finger Searching (Extended Abstract)

• Richard Cole 0001
• Arvind Raghunathan

The technique of speeding up access into search structures by maintaining fingers that point to various locations of the search structure is considered. The problem of choosing, in a large search structure, locations at which to maintain fingers is treated. In particular, a server problem in which k servers move along a line segment of length m, where m is the number of keys in the search structure, is addressed. Since fingers may be arbitrarily copied, a server is allowed to jump, or fork, to a location currently occupied by another server. Online algorithms are presented and their competitiveness analyzed. It is shown that the case in which k=2 behaves differently from the case in which k>or=3, by showing that there is a four-competitive algorithm for k=2 that never forks its fingers. For k>or=3, it is shown that any online algorithm that does not fork its fingers can be at most Omega (m/sup 1/2/)-competitive. The main result is that for k=3 there is an online algorithm that forks and is constant competitive (independent of m, the size of the search structure). The algorithm is simple and implementable. >

STOC Conference 1990 Conference Paper

Online Algorithms for Locating Checkpoints

• Marshall W. Bern
• Daniel H. Greene
• Arvind Raghunathan
• Madhu Sudan 0001

FOCS Conference 1988 Conference Paper

Constructive Results from Graph Minors: Linkless Embeddings

• Rajeev Motwani 0001
• Arvind Raghunathan
• Huzur Saran

A formal study of three-dimensional topological graph theory is initiated. The problem of deciding whether a graph can be embedded in 3-space so that no collection of vertex-disjoint cycles is topologically linked is considered first. The Robertson-Seymour Theory of Graph Minors is applicable to this problem and guarantees the existence of an O(n/sup 3/) algorithm for the decision problem. However, not even a finite-time decision procedure was known for this problem. A small set of forbidden minors for linkless embeddable graphs is exhibited, and it is shown that any graph with these minors cannot be embedded without linked cycles. It is further established that any graph that does not contain these minors is embeddable without linked cycles. Thus, an O(n/sup 3/) algorithm for the decision problem is demonstrated. It is believed that the proof technique will lead to an algorithm for actually embedding a graph, provided it does not contain the forbidden minors. >