Related papers: Newton methods for k-order Markov Constrained Moti…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
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…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Placing robots outside controlled conditions requires versatile movement representations that allow robots to learn new tasks and adapt them to environmental changes. The introduction of obstacles or the placement of additional robots in…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…