Related papers: Active-set Newton methods and partial smoothness
We consider online optimization problems with time-varying linear equality constraints. In this framework, an agent makes sequential decisions using only prior information. At every round, the agent suffers an environment-determined loss…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex…
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then…
Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications,…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality…
Automated machine learning (AutoML) methods improve upon existing models by optimizing various aspects of their design. While present methods focus on hyperparameters and neural network topologies, other aspects of neural network design can…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
This study proposes an efficient Newton-type method for the optimal control of switched systems under a given mode sequence. A mesh-refinement-based approach is utilized to discretize continuous-time optimal control problems (OCPs) and…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…