Related papers: Variable reduction as a nonlinear preconditioning …
We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…
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…
The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines an evolution equation so that in the asymptotic limit a…
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…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
Newton-type methods are typically analyzed under Lipschitz continuity of the Hessian, an assumption that can fail for objectives with higher-order or polynomial growth. We introduce a class of nonlinearly preconditioned Newton methods that…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
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…
We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
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…
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…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be found, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…