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The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently…
In a tie-breaker design (TBD), subjects with high values of a running variable are given some (usually desirable) treatment, subjects with low values are not, and subjects in the middle are randomized. TBDs are intermediate between…
Body-centered Cubic (BCC) lattice structures demonstrate promising performance for applications that require simultaneous mechanical energy absorption and thermal management. However, current optimization approaches are typically confined…
In this paper, we study mechanical optimal control problems on a given Riemannian manifold $(Q,g)$ in which the cost is defined by a general cometric $\tilde{g}$. This investigation is motivated by our studies in robotics, in which we…
A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are…
We give query complexity lower bounds for convex optimization and the related feasibility problem. We show that quadratic memory is necessary to achieve the optimal oracle complexity for first-order convex optimization. In particular, this…
We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of…
The ability to design effective experiments is crucial for obtaining data that can substantially reduce the uncertainty in the predictions made using computational models. An optimal experimental design (OED) refers to the choice of a…
Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…
The proton exchange membrane fuel cell (PEMFC) output relies on the transport behavior within the cathode gas channels. Current designs remain inadequate as they often rely on heuristic modifications of existing layouts or designer…
Inverse design has enabled the systematic design of ultra-compact and high-performance nanophotonic components. Yet enforcing foundry design rules during inverse design remains a major challenge, as optimized devices frequently violate…
AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global…
We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation…
Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…
Optimal behaviours of a system to perform a specific task can be achieved by leveraging the coupling between trajectory optimization, stabilization, and design optimization. This approach is particularly advantageous for underactuated…
This paper presents a scalable method for improving the solutions of AC Optimal Power Flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The focus of the paper is on…
We present an aeroacoustic shape optimization framework that relies on high-order Flux Reconstruction (FR), the gradient-free Mesh Adaptive Direct Search (MADS) optimization algorithm, and Large Eddy Simulation (LES). Our parallel…
The mechanical response of interpenetrating phase composites (IPCs) with stochastic spinodal topologies is investigated experimentally and numerically. Model polymeric systems are fabricated by Polyjet multi-material printing, with the…