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A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
In this paper, we present a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance that is applicable to any system of partial differential equations. In particular, we parameterize…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly…
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative…
Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…
Statistical design of experiments is widely used in scientific and industrial investigations. A generalized minimum aberration (GMA) orthogonal array is optimum under the well-established, so-called GMA criterion, and such an array can…
We develop a geometric convergence theory for neural-network optimization within the minimizing movement scheme (MMS) framework. Reformulating each neural MMS step as a minimization over the set of increments in a Hilbert space, we show…
Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…