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CSPTRQ is an interesting problem and its has attracted much attention. The CSPTRQ is a variant of the traditional PTRQ. As objects moving in a constrained-space are common, clearly, it can also find many applications. At the first sight,…
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
Techniques for finding regularized solutions to underdetermined linear systems can be viewed as imposing prior knowledge on the unknown vector. The success of modern techniques, which can impose priors such as sparsity and non-negativity,…
Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope…
A trace ratio optimization problem over the Stiefel manifold is investigated from the perspectives of both theory and numerical computations. At least three special cases of the problem have arisen from Fisher linear discriminant analysis,…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…
Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…
It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
The problem of attitude tracking using rotation matrices is addressed using an approach which combines inverse optimality and $\mathcal{L}_{2}$ disturbance attenuation. Conditions are provided which solve the inverse optimal nonlinear…
While the constant radial acceleration problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to a time parameter, has eluded…
Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…
The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…
The problem of Reinforcement Learning (RL) in an unknown nonlinear dynamical system is equivalent to the search for an optimal feedback law utilizing the simulations/ rollouts of the dynamical system. Most RL techniques search over a…
A novel solution is obtained to solve the rigid 3D registration problem, motivated by previous eigen-decomposition approaches. Different from existing solvers, the proposed algorithm does not require sophisticated matrix operations e.g.…