Related papers: A globalized inexact semismooth Newton method for …
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
In this paper, we propose a third-order Newton's method which in each iteration solves a semidefinite program as a subproblem. Our approach is based on moving to the local minimum of the third-order Taylor expansion at each iteration,…
Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other…
Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
Subgradient methods comprise a fundamental class of nonsmooth optimization algorithms. Classical results show that certain subgradient methods converge sublinearly for general Lipschitz convex functions and converge linearly for convex…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
This article presents a second-order fully distributed optimization algorithm, HBNET-GIANT, driven by heavy-ball momentum, for $L$-smooth and $\mu$-strongly convex objective functions. A rigorous convergence analysis is performed, and we…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve…
In this paper, we propose a distributed second- order method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by…
We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with…
In this work we present and discuss a possible globalization concept for Newton-type methods. We consider nonlinear problems $f(x)=0$ in $\mathbb{R}^{n}$ using the concepts from ordinary differential equations as a basis for the proposed…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…