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An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…

Optimization and Control · Mathematics 2022-04-26 Frank E. Curtis , Qi Wang

Physics-informed machine learning and inverse modeling require the solution of ill-conditioned non-convex optimization problems. First-order methods, such as SGD and ADAM, and quasi-Newton methods, such as BFGS and L-BFGS, have been applied…

Numerical Analysis · Mathematics 2021-05-18 Kailai Xu , Eric Darve

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…

Optimization and Control · Mathematics 2026-02-16 Hanfeng Zeng , Wenqing Ouyang , Andre Milzarek

We introduce iR2N, a modified proximal quasi-Newton method for minimizing the sum of a smooth function $f$ and a lower semi-continuous prox-bounded function $h$, allowing inexact evaluations of $f$, its gradient, and the associated proximal…

Optimization and Control · Mathematics 2025-12-17 Nathan Allaire , Sébastien Le Digabel , Dominique Orban

This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theoretical framework for inexact proximal point (IPP) methods…

Optimization and Control · Mathematics 2025-06-03 Minxin Zhang , Fuqun Han , Yat Tin Chow , Stanley Osher , Hayden Schaeffer

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…

Optimization and Control · Mathematics 2022-01-05 Shigeng Sun , Jorge Nocedal

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

Optimization and Control · Mathematics 2025-04-01 Hao Wang , Xiangyu Yang , Yichen Zhu

We propose a globally convergent trust-region bundle method for minimizing lower-$C^2$ functions using higher-order cutting-plane models. Under certain growth assumptions on the objective around its minimum, the method is able to compute…

Optimization and Control · Mathematics 2026-03-26 Bennet Gebken , Michael Ulbrich

In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and…

Optimization and Control · Mathematics 2025-03-04 Yassine Nabou , Ion Necoara

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…

Optimization and Control · Mathematics 2025-10-21 Dânâ Davar , Geovani Nunes Grapiglia

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton…

Optimization and Control · Mathematics 2013-09-16 Richard H. Byrd , Jorge Nocedal , Figen Oztoprak

This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain…

Optimization and Control · Mathematics 2026-05-14 Yiwen Chen , Warren Hare , Amy Wiebe

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

Optimization and Control · Mathematics 2016-02-08 Hideaki Iiduka

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place…

Optimization and Control · Mathematics 2015-08-04 Jean-Hubert Hours , Colin N. Jones

We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas.…

Optimization and Control · Mathematics 2024-04-24 Ewa Bednarczuk , Giovanni Bruccola , Gabriele Scrivanti , The Hung Tran

Manifold optimization has recently gained significant attention due to its wide range of applications in various areas. This paper introduces the first Riemannian trust region method for minimizing an SC$^1$ function, which is a…

Optimization and Control · Mathematics 2024-06-03 Chenyu Zhang , Rufeng Xiao , Wen Huang , Rujun Jiang

This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…

Optimization and Control · Mathematics 2025-11-26 Yuge Ye , Qingna Li

We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…

Numerical Analysis · Mathematics 2018-06-20 Martin Neuenhofen

We propose a stochastic trust-region method for unconstrained nonconvex optimization that incorporates stochastic variance-reduced gradients (SVRG) to accelerate convergence. Unlike classical trust-region methods, the proposed algorithm…

Optimization and Control · Mathematics 2026-01-22 Yuchen Fang , Xinshou Zheng , Javad Lavaei