Related papers: An interior point method for nonlinear constrained…
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using the more efficient online algorithms through time-varying optimization. The idea lies in that…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
In this article, we present a problem of nonlinear constraint optimization with equality and inequality constraints. Objective functions are defined to be nonlinear and optimizers may have a lower and upper bound. We solve the optimization…
We study first-order methods (FOMs) for solving \emph{composite nonconvex nonsmooth} optimization with linear constraints. Recently, the lower complexity bounds of FOMs on finding an ($\varepsilon,\varepsilon$)-KKT point of the considered…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…
In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality…
We introduce a novel distributed derivative-free optimization framework that is resilient to stragglers. The proposed method employs coded search directions at which the objective function is evaluated, and a decoding step to find the next…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
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…