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A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…
In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of…
In this paper we briefly review two recent use-cases of quantum optimization algorithms applied to hard problems in finance and economy. Specifically, we discuss the prediction of financial crashes as well as dynamic portfolio optimization.…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
We present recent results on optimal algorithms for numerical integration and several open problems. The paper has six parts: 1. Introduction 2. Lower Bounds 3. Universality 4. General Domains 5. iid Information 6. Concluding Remarks
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
This is a slightly revised version of the Presidential address (General) delivered at the 84th Annual Conference of the Indian Mathematical Society held at Jammu, India during November 2018.
This is a PhD dissertation on the latest numerical quantum estimation schemes as of 2012, submitted to the National University of Singapore. The main content of the thesis focuses on accessing quantum information with informationally…
Networks-on-chip (NoCs) have become the standard for interconnect solutions in industrial designs ranging from client CPUs to many-core chip-multiprocessors. Since NoCs play a vital role in system performance and power consumption,…
Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the…
Quantum computing is becoming strategically relevant to finance because several core financial bottlenecks are already defined by combinatorial search, expectation estimation, rare-event analysis, representation learning, and long-horizon…
This is a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019. It is supposed to be a concise (and therefore not comprehensive) and pragmatic course on applied holography and…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.
ICOOOLPS'2006 was the first edition of ECOOP-ICOOOLPS workshop. It intended to bring researchers and practitioners both from academia and industry together, with a spirit of openness, to try and identify and begin to address the numerous…
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
The community of program optimisation and analysis, code performance evaluation, parallelisation and optimising compilation has published since many decades hundreds of research and engineering articles in major conferences and journals.…
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…