Robustness analysis for identification and control of nonlinear systems by Tobenkin, Mark M

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Constrained Consensus and Optimization in Multi-Agent Networks by Nedic, Angelia, Ozdaglar, Asuman E., Parrilo, Pablo A.

“…Our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets. To highlight the effects of constraints, we first consider a constrained consensus problem and present a distributed "projected consensus algorithm" in which agents combine their local averaging operation with projection on their individual constraint sets. …”
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Mixed-integer convex optimization : outer approximation algorithms and modeling power by Lubin, Miles (Miles C.)

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Incorporation of biological factors in radiation therapy treatment planning by Brooke, M

“…</p> <p>This thesis proposes novel methods and recommendations for the inclusion of radiobiological factors in treatment planning through (1) a variable but pragmatic RBE model based on DNA double strand break induction, and (2) a flexible, projection-based inverse planning algorithm, suited to non-convex settings, that comprehensively addresses dose-volume effects through the exact modeling of DVCs. …”

Adversarial hypothesis testing and a quantum stein's lemma for restricted measurements by Brandao, Fernando G.S.L., Harrow, Aram W., Lee, James R., Peres, Yuval

“…Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p ∈ P or from a distribution q ∈ Q and wants to decide from which set the points were sampled. …”
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Introducing ICEDAP: An ‘Iterative Coastal Embayment Delineation and Analysis Process’ with Applications for the Management of Coastal Change by Nicholas B. Wellbrock, Nathalie W. Jung, David P. Retchless, Timothy M. Dellapenna, Victoria L. Salgado

“…We then applied ICEDAP to the coast of South Korea, and found that coastal habitat change was particularly profound within embayed regions identified using an 8 km epsilon convexity setting (denoting a moderate distance from the coast and degree of enclosure by surrounding land areas). …”
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Improvements to sparse signal processing in compressive sensing and other methods by Huang, Honglin

“…Finally, a simple iterative reconstruction method based on Projection Onto Convex Sets (POCS) is designed to effectively encode the object error. …”
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A MLEM-TV-MRP Algorithm for Fast Neutron Computed Tomography Reconstruction of High Statistical Noise and Sparse Sampling by Sangang Li, Zhengyun Dong, Quan Gan, Shengpeng Yu, Qi Yang, Jing Song

“…SNR value of MLEM-TV-MRP showed an increase of about 62%, 40.7%, 36.7%, and 12.6% respectively as compared to the single-use of MLEM, MLEM-MRP, TV-POCS (projection on convex sets) and MLEM-TV. Also, the profile of the MLEM-TV-MRP algorithm is found to be closest to that of a reference image. …”
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Smoothness and Adaptivity in Nonlinear Optimization for Machine Learning Applications by Li, Haochuan

“…In particular, we obtain the classical convergence rates for gradient descent (GD), stochastic gradient descent (SGD), and Nesterov’s accelerated gradient method (NAG) in the convex or non-convex settings under this general smoothness condition. …”
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Low-Rank Gradient Descent by Romain Cosson, Ali Jadbabaie, Anuran Makur, Amirhossein Reisizadeh, Devavrat Shah

“…Therefore, when <inline-formula><tex-math notation="LaTeX">$r \ll p$</tex-math></inline-formula>, <monospace>LRGD</monospace> provides significant improvement over the known complexities of <inline-formula><tex-math notation="LaTeX">${\mathcal {O}}(p \log (1/\epsilon))$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${\mathcal {O}}(p/\epsilon ^{2})$</tex-math></inline-formula> of <monospace>GD</monospace> in the strongly convex and non-convex settings, respectively. Furthermore, we formally characterize the classes of exactly and approximately low-rank functions. …”
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Applications of optimization in probability, finance and revenue management by Popescu, Ioana

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Harmonic maps and associated energy functionals by Tošić, O

“…Nearest-point projections to convex sets are natural objects of study that fall outside the scope of this work. …”

Average revenue efficiency and optimal scale sizes in stochastic data envelopment analysis: A case study of post offices by Leila Parhizkar Miyandehi, Alireza Amirteimoori, Sohrab Kordrostami, Mansour Soufi

“…Additionally, the ARE is defined for both convex and non-convex sets, independent of returns to scale and the assumption that the vector of input-output prices of units is uniform. …”
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