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Decomposition of large matrix inequalities for matrices with chordal sparsity graph has been recently used by Kojima et al.\ \cite{kim2011exploiting} to reduce problem size of large scale semidefinite optimization (SDO) problems and thus…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the…
Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…
This paper presents a novel algorithm to incorporate orbital parameters into radar ambiguity function expressions by extending the standard ambiguity function to match Keplerian two-body orbits. A coherent orbital matched-filter will…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the…
This paper introduces a set of customizable and novel cost functions that enable the user to easily specify desirable robot formations, such as a ``high-coverage'' infrastructure-inspection formation, while maintaining high relative pose…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization…
We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most…
This paper aims to design a set of transmitting waveforms in cognitive colocated Multi-Input Multi-Output (MIMO) radar systems considering the simultaneous minimization of spatial- and the range- Integrated Sidelobe Level Ratio (ISLR). The…
Many robotics and mapping systems contain multiple sensors to perceive the environment. Extrinsic parameter calibration, the identification of the position and rotation transform between the frames of the different sensors, is critical to…
Well-designed data visualizations can lead to more powerful and intuitive processing by a viewer. To help a viewer intuitively compare values to quickly generate key takeaways, visualization designers can manipulate how data values are…
Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.…