Related papers: Global Stochastic Optimization of Stellarator Coil…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
This paper addresses the stabilization problem of stochastic jump systems (SJSs) closed by a generally sampled controller. Because of the controller's switching and state both sampled, it is challenging to study its stabilization. A new…
This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost. In our previous work, we have shown that by utilizing…
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…
A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
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…
We introduce a doubly stochastic proximal gradient algorithm for optimizing a finite average of smooth convex functions, whose gradients depend on numerically expensive expectations. Our main motivation is the acceleration of the…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…
Many problems arise in computational biology can be reduced to the minimization of energy function, that determines on the geometry of considered molecule. The solution of this problem allows in particular to solve folding and docking…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…