Related papers: Continuation Path with Linear Convergence Rate
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be very efficient in solving high dimensional problems. Even though…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
We present a new optimization-theoretic approach to analyzing Follow-the-Leader style algorithms, particularly in the setting where perturbations are used as a tool for regularization. We show that adding a strongly convex penalty function…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
Machine learning algorithms typically rely on optimization subroutines and are well-known to provide very effective outcomes for many types of problems. Here, we flip the reliance and ask the reverse question: can machine learning…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost…
We present a sample-based motion planning algorithm specialised to a class of underactuated systems using path parameterisation. The structure this class presents under a path parameterisation enables the trivial computation of dynamic…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Trajectory planning for mobile robots in cluttered environments remains a major challenge due to narrow passages, where conventional methods often fail or generate suboptimal paths. To address this issue, we propose the adaptive trajectory…