Related papers: How-to Augmented Lagrangian on Factor Graphs
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…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
In this paper we present a systematic study of photonic bandgap engineering using aperiodic lattices (ALs). Up to now ALs have tended to be defined by specific formulae (e.g. Fibonacci, Cantor), and theories have neglected other useful ALs…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation…
In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…
Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…
Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate…
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…
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…
Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or…
This paper consists of a tutorial on the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) and its application to distributed model predictive control (MPC). The focus is - for simplicity of presentation - on…
The paper addresses the problem of optimizing a class of composite functions on Riemannian manifolds and a new first order optimization algorithm (FOA) with a fast convergence rate is proposed. Through the theoretical analysis for FOA, it…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…