Related papers: A Nonlinear Acceleration Method for Iterative Algo…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based…
This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented.…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a…
This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…
We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning…
For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for…
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in Quantum Optimal Control Theory (QOCT). We show how the non-linear equations of QOCT can be viewed as a "fixed-point"…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…
In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…