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We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables…
We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…
The split common fixed point problems has found its applications in various branches of mathematics both pure and applied. It provides us a unified structure to study a large number of nonlinear mappings. Our interest here is to apply these…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
In this paper an explicit algorithm is proposed for solving an equilibrium problem whose associated bifunction is pseudomonotone and satisfies a Lipschitz-type condition. Contrary to many algorithms, our algorithm is done without using…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
We study convergence rates of the classic proximal bundle method for a variety of nonsmooth convex optimization problems. We show that, without any modification, this algorithm adapts to converge faster in the presence of smoothness or a…