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Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…
We propose novel algorithms combining accelerated gradient flows with linearized projection-free treatments of non-convex constraints and BDF pseudo-temporal discretization for quadratic energy minimization. A general framework is developed…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable…
We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method…
In this paper we consider the composite self-concordant (CSC) minimization problem, which minimizes the sum of a self-concordant function $f$ and a (possibly nonsmooth) proper closed convex function $g$. The CSC minimization is the…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…
Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…
Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding…
In this paper, we propose an accelerated quasi-Newton proximal extragradient (A-QPNE) method for solving unconstrained smooth convex optimization problems. With access only to the gradients of the objective, we prove that our method can…
This paper considers a class of convex constrained nonsmooth convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a general nonsmooth but…
In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the…
Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly convex function $f$ is known to reduce $f({\bf x}_k)-f({\bf x}^*)$ by a factor of $\epsilon\in(0,1)$ after $k=O(\sqrt{L/\ell}\log(1/\epsilon))$ iterations, where…
In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…
We present a method for optimizing the location of the fermion ground-state nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient descent (PGD). A PGD iteration shifts the parameters of an arbitrary node-fixing…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics…
Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are…
We develop numerical methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta…
We focus on the problem of minimizing the sum of smooth component functions (where the sum is strongly convex) and a non-smooth convex function, which arises in regularized empirical risk minimization in machine learning and distributed…