Related papers: Sequential Hierarchical Least-Squares Programming …
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where the memory footprint of the operator is a concern. Discretizing images in…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…
The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given…
We consider the fundamental problem of maximizing a general quadratic function over an ellipsoidal domain, also known as the trust region problem. We give the first provable linear-time (in the number of non-zero entries of the input)…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
In this paper, we propose an efficient sieving based secant method to address the computational challenges of solving sparse optimization problems with least-squares constraints. A level-set method has been introduced in [X. Li, D.F. Sun,…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
We construct a soft thresholding operation for rank reduction of hierarchical tensors and subsequently consider its use in iterative thresholding methods, in particular for the solution of discretized high-dimensional elliptic problems. The…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with…
We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian…
In this paper, we develop an optimization-based framework for solving coupled forward-backward stochastic differential equations. We introduce an integral-form objective function and prove its equivalence to the error between consecutive…