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The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
For solving large-scale consistent linear system, we combine two efficient row index selection strategies with Kaczmarz-type method with oblique projection, and propose a greedy randomized Kaczmarz method with oblique projection (GRKO) and…
Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…
We present a fast two-phase algorithm for super-resolution with strong theoretical guarantees. Given the low-frequency part of the spectrum of a sequence of impulses, Phase I consists of a greedy algorithm that roughly estimates the impulse…
Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…
In this effort we introduce and analyze a novel reduced basis approach, used to construct an approximating subspace for a given set of data. Our technique, which we call the Natural Greedy Algorithm (NGA), is based on a recursive approach…
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…
*The following abbreviates the abstract. Please refer to the thesis for the full abstract.* After a disaster, locating and extracting victims quickly is critical because mortality rises rapidly after the first two days. To assist search and…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
Solutions to hyperbolic systems comprise waves propagating at finite speeds. When wave propagation is predominantly unidirectional, one-way wave equations can be used to evolve only the right-going solution by removing support for…
We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making…
In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…
By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of…
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…
Routing and scheduling problems with time windows have long been important optimization problems for logistics and planning. Many classical heuristics and exact methods exist for such problems. However, there are no satisfactory methods for…