Related papers: Approximate matrix and tensor diagonalization by u…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We study the orthogonal polynomials associated with the equilibrium measure, in logarithmic potential theory, living on the attractor of an Iterated Function System. We construct sequences of discrete measures, that converge weakly to the…
The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…
Tensor optimization is crucial to massive machine learning and signal processing tasks. In this paper, we consider tensor optimization with a convex and well-conditioned objective function and reformulate it into a nonconvex optimization…
Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor…
Main objects of the paper are stationary and weak KAM Hamilton-Jacobi equations on the finite-dimensional torus. The key idea of the paper is to replace the underlying calculus of variations problems with continuous time Markov decision…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…