Related papers: Projected nonlinear least squares for exponential …
In the total least squares problem, one is given an $m \times n$ matrix $A$, and an $m \times d$ matrix $B$, and one seeks to "correct" both $A$ and $B$, obtaining matrices $\hat{A}$ and $\hat{B}$, so that there exists an $X$ satisfying the…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…
Planes are generally used in 3D reconstruction for depth sensors, such as RGB-D cameras and LiDARs. This paper focuses on the problem of estimating the optimal planes and sensor poses to minimize the point-to-plane distance. The resulting…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Predict and optimize is an increasingly popular decision-making paradigm that employs machine learning to predict unknown parameters of optimization problems. Instead of minimizing the prediction error of the parameters, it trains…