Related papers: Two-derivative error inhibiting schemes with post-…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
Many real-world decisions are made under uncertainty by solving optimization problems using predicted quantities. This predict-then-optimize paradigm has motivated decision-focused learning, which trains models with awareness of how the…
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…
Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one…
In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
In this paper, we present a sequential sampling-based algorithm for the two-stage distributionally robust linear programming (2-DRLP) models. The 2-DRLP models are defined over a general class of ambiguity sets with discrete or continuous…
The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. Based on the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
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…
We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line…
In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main assumption being that the third derivative of the objective…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…
In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
High order strong stability preserving (SSP) time discretizations are often needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial discretizations specially designed for the solution of…