Related papers: CLARSTA: A random subspace trust-region algorithm …

Worst-case complexity guarantees for nonconvex optimization algorithms have been a topic of growing interest. Multiple frameworks that achieve the best known complexity bounds among a broad class of first- and second-order strategies have…

Randomized Fast Subspace Descent (RFASD) Methods are developed and analyzed for smooth and non-constraint convex optimization problems. The efficiency of the method relies on a space decomposition which is stable in $A$-norm, and meanwhile,…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze…

In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore…

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and…

Trust Region Policy Optimization (TRPO) is an iterative method that simultaneously maximizes a surrogate objective and enforces a trust region constraint over consecutive policies in each iteration. The combination of the surrogate…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…

Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be…

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…

We present a novel derivative-free interpolation based optimization algorithm. A trust-region method is used where a surrogate model is realized via an interpolation framework. The framework for interpolation is provided by Universal…

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…