Related papers: An Augmented Lagrangian Approach to Composite Prob…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…
In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…
Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
In this work, we shed light on the so-called Kaczmarz method for solving Linear System (LS) and Linear Feasibility (LF) problems from a optimization point of view. We introduce well-known optimization approaches such as Lagrangian penalty…
Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Magnetic Resonance Imaging (MRI) is one of the fields that the compressed sensing theory is well utilized to reduce the scan time significantly leading to faster imaging or higher resolution images. It has been shown that a small fraction…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangians for cone constrained programs within a unified…
Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
A nonlinear MPC framework is presented that is suitable for dynamical systems with sampling times in the (sub)millisecond range and that allows for an efficient implementation on embedded hardware. The algorithm is based on an augmented…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…