Related papers: The Effective Countable Generalized Moment Problem
We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
We consider the problem of global optimization of a function over a continuous domain. In our setup, we can evaluate the function sequentially at points of our choice and the evaluations are noisy. We frame it as a continuum-armed bandit…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these…
Generalized and Simulated Method of Moments are often used to estimate structural Economic models. Yet, it is commonly reported that optimization is challenging because the corresponding objective function is non-convex. For smooth…
Recently, the precise performance of the Generalized LASSO algorithm for recovering structured signals from compressed noisy measurements, obtained via i.i.d. Gaussian matrices, has been characterized. The analysis is based on a framework…
The constrained generalized maximum-entropy sampling problem (CGMESP) is to select an order-s principal submatrix from an order-n covariance matrix, subject to some linear side constraints, so as to maximize the product of its t greatest…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the…
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…
We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism. This limit gives rise to a multi-marginal optimal transport (MMOT) problem. Here the marginal state space…
We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…
In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor-Hood elements, under the assumption of the…
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…