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We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
Electron cryomicroscopy (cryo-EM) is an imaging technique widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the…
The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that…
Lightweight inference is critical for biomolecular structure prediction and downstream tasks, enabling efficient real-world deployment and inference-time scaling for large-scale applications. While AF3 and its variants (e.g., Protenix,…
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and…
Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this…
Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their…
Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this…
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…
We develop and analyze Riemannian optimization methods for computing ground states of rotating multicomponent Bose-Einstein condensates, defined as minimizers of the Gross-Pitaevskii energy functional. To resolve the non-uniqueness of…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…
Gradient boosting, a method of building additive ensembles from weak learners, has established itself as a practical and theoretically-motivated approach to approximate functions, especially using decision tree weak learners. Comparable…