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We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Deep convolutional neural networks have liberated its extraordinary power on various tasks. However, it is still very challenging to deploy state-of-the-art models into real-world applications due to their high computational complexity. How…
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities.…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of…
In the context of the graph matching problem we propose a novel method for projecting a matrix $Q$, which may be a doubly stochastic matrix, to a permutation matrix $P.$ We observe that there is an intuitve mapping, depending on a given…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
Estimating the pose of a camera with respect to a 3D reconstruction or scene representation is a crucial step for many mixed reality and robotics applications. Given the vast amount of available data nowadays, many applications constrain…
Convolutional Neural Networks (CNNs) are state-of-the-art in numerous computer vision tasks such as object classification and detection. However, the large amount of parameters they contain leads to a high computational complexity and…
In this paper, we consider the computational protein design (CPD) problem, which is usually modeled as 0/1 programming and is extremely challenging due to its combinatorial properties. As a quadratic semi-assignment problem (QSAP), the CPD…
To accelerate deep CNN models, this paper proposes a novel spatially adaptive framework that can dynamically generate pixel-wise sparsity according to the input image. The sparse scheme is pixel-wise refined, regional adaptive under a…
In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must…
We propose two quantum algorithms for a problem in bioinformatics, position weight matrix (PWM) matching, which aims to find segments (sequence motifs) in a biological sequence such as DNA and protein that have high scores defined by the…
Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution…