Related papers: Two-level trust-region method with random subspace…

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…

This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…

Generalized trust-region subproblem (GT) is a nonconvex quadratic optimization with a single quadratic constraint. It reduces to the classical trust-region subproblem (T) if the constraint set is a Euclidean ball. (GT) is polynomially…

We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region…

Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs, a fundamental problem in many real-world applications. In active learning settings with limited initial data, we aim…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem potentially being nonsmooth. We develop a two-timescale…

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…

Trust-region methods (TR) can converge quadratically to minima where the Hessian is positive definite. However, if the minima are not isolated, then the Hessian there cannot be positive definite. The weaker…

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible…

In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…

In this work, we consider solving optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Sequential Quadratic Programming method to find both first- and second-order stationary…

Large language models often struggle with complex long-horizon analytical tasks over unstructured tables, which typically feature hierarchical and bidirectional headers and non-canonical layouts. We formalize this challenge as Deep Tabular…

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data…

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth…

We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…

Gray-box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black-box models lacking analytic derivatives, remains a challenge. Trust-region (TR) methods provide a robust…