publications

2024

1. COAP

   Nonsmooth projection-free optimization with functional constraints

   Kamiar Asgari, and Michael J. Neely

   Computational Optimization and Applications, Dec 2024

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   This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank–Wolfe algorithm and its variants already avoid projections, they are primarily designed for smooth objective functions. In contrast, our proposed algorithm can handle nonsmooth problems with general convex functional inequality constraints. It achieves an }}\backslashepsilon }}-suboptimal solution in }}\backslashmathcal {O}(\backslashepsilon ^{-2})}}iterations, with each iteration requiring only a single (potentially inexact) Linear Minimization Oracle call and a (possibly inexact) subgradient computation. This performance is consistent with existing lower bounds. Similar performance is observed when deterministic subgradients are replaced with stochastic subgradients. In the special case where there are no functional inequality constraints, our algorithm competes favorably with a recent nonsmooth projection-free method designed for constraint-free problems. Our approach utilizes a simple separation scheme in conjunction with a new Lagrange multiplier update rule.

2020

1. POMACS

   Bregman-Style Online Convex Optimization with EnergyHarvesting Constraints

   Kamiar Asgari, and Michael J. Neely

   Proc. ACM Meas. Anal. Comput. Syst., Nov 2020

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   This paper considers online convex optimization (OCO) problems where decisions are constrained by available energy resources. A key scenario is optimal power control for an energy harvesting device with a finite capacity battery. The goal is to minimize a time-average loss function while keeping the used energy less than what is available. In this setup, the distribution of the randomly arriving harvestable energy (which is assumed to be i.i.d.) is unknown, the current loss function is unknown, and the controller is only informed by the history of past observations. A prior algorithm is known to achieve O(sqrtT ) regret by using a battery with an O(sqrtT ) capacity. This paper develops a new algorithm that maintains this asymptotic trade-off with the number of time steps T while improving dependency on the dimension of the decision vector from O(sqrtn ) to O(sqrtłog(n) ). The proposed algorithm introduces a separation of the decision vector into amplitude and direction components. It uses two distinct types of Bregman divergence, together with energy queue information, to make decisions for each component.

2. fams

   Identifying Arguments of Space-Time Fractional Diffusion: Data-Driven Approach

   Mohamed Ridha Znaidi, Gaurav Gupta, Kamiar Asgari, and 1 more author

   Frontiers in Applied Mathematics and Statistics, Nov 2020

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   A plethora of complex dynamical systems from disordered media to biological systems exhibit mathematical characteristics (e.g., long-range dependence, self-similar and power law magnitude increments) that are well-fitted by fractional partial differential equations (PDEs). For instance, some biological systems displaying an anomalous diffusion behavior, which is characterized by a non-linear mean-square displacement relation, can be mathematically described by fractional PDEs. In general, the PDEs represent various physical laws or rules governing complex dynamical systems. Since prior knowledge about the mathematical equations describing complex dynamical systems in biology, healthcare, disaster mitigation, transportation, or environmental sciences may not be available, we aim to provide algorithmic strategies to discover the integer or fractional PDEs and their parameters from system’s evolution data. Toward deciphering non-trivial mechanisms driving a complex system, we propose a data-driven approach that estimates the parameters of a fractional PDE model. We study the space-time fractional diffusion model that describes a complex stochastic process, where the magnitude and the time increments are stable processes. Starting from limited time-series data recorded while the system is evolving, we develop a fractional-order moments-based approach to determine the parameters of a generalized fractional PDE. We formulate two optimization problems to allow us to estimate the arguments of the fractional PDE. Employing extensive simulation studies, we show that the proposed approach is effective at retrieving the relevant parameters of the space-time fractional PDE. The presented mathematical approach can be further enhanced and generalized to include additional operators that may help to identify the dominant rule governing the measurements or to determine the degree to which multiple physical laws contribute to the observed dynamics.