Related papers: Nonlinear Schwarz preconditioning for nonlinear op…
Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using…
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique.…
This paper presents the Safe Sequential Quadratically Constrained Quadratic Programming (SS-QCQP) algorithm, a first-order method for smooth inequality-constrained nonconvex optimization that guarantees feasibility at every iteration. The…
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz…
Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or…
We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the…
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…
The discretization of Cahn-Hilliard equation with obstacle potential leads to a block 2 by 2 non-linear system, where the p1, 1q block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper introduces and develops novel coderivative-based Newton methods with Wolfe linesearch conditions to solve various classes of problems in nonsmooth optimization. We first propose a generalized regularized Newton method with Wolfe…
In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
We derive nonlinear acceleration methods based on the limited memory BFGS (L-BFGS) update formula for accelerating iterative optimization methods of alternating least squares (ALS) type applied to canonical polyadic (CP) and Tucker tensor…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular integral equations are considered. We prove that the…
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 class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…