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Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Accurate electronic structure calculations might be one of the most anticipated applications of quantum computing.The recent landscape of quantum simulations within the Hartree-Fock approximation raises the prospect of substantial theory…
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
We introduce a perturbative approximation to the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. The method, termed DFT/MRCI(2), results from the application of quasi-degenerate…
The slow convergence rate and pathological curvature issues of first-order gradient methods for training deep neural networks, initiated an ongoing effort for developing faster $\mathit{second}$-$\mathit{order}$ optimization algorithms…
By introducing the "comparison and replacement" (CNR) operation, we propose a general-purpose pure quantum approximate optimization algorithm and derive its core optimization mechanism quantitatively. The algorithm is constructed to a…
We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian,…
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…
Accurately describing strong electron correlation in complex systems remains a prominent challenge in computational chemistry as near-term quantum algorithms treating total correlation often require prohibitively deep circuits. Here we…
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new…
Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative…
Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales…
Large-scale convolutional neural networks (CNNs) suffer from very long training times, spanning from hours to weeks, limiting the productivity and experimentation of deep learning practitioners. As networks grow in size and complexity,…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
UGA-SSMRPT2, the spin-free perturbative analogue of Mukerjee's State-Specific Multireference Coupled Cluster Theory (MkMRCC) is known to be successful for size-extensive and intruder-free construction of dissociation curves. This work…
Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing…
In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally Lipschitz differentiable (possibly nonconvex) function,…