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Jul 2026

New Globalized Newton-Type Methods for Nonconvex Optimization Problems

This paper proposes a general line-search Newton framework for unconstrained optimization that avoids repeated Hessian regularization by exploiting the Newton direction only when it is well-defined and suitable and provides the first Newton-type algorithm together with a comprehensive convergence analysis for this important class of nonconvex optimization problems.

Phat Thanh Vo, Tuyen Tran · 0 citations
Preprint Aug 2026

A Wolfe-Type Spectral Conjugate Gradient Method for Nonsmooth Convex Optimization Problems

This paper proposes a Wolfe-type spectral conjugate gradient method for nonsmooth convex optimization, built on the Moreau-Yosida regularization of the objective function. The method combines a safeguarded spectral parameter with a Dai-Kou-type conjugate parameter, and uses a Wolfe-type line search compatible with the inexact gradients that the regularization produces. We establish global convergence of the method, together with an R-linear convergence rate under an additional strong-convexity assumption. The method is evaluated on standard nonsmooth optimization benchmarks and on large-scale problems, and compared against several existing conjugate gradient and bundle-type methods. The results show that the proposed method performs competitively overall, matching or outperforming existing methods on most problems tested, while a few specific limitations of the current implementation are also identified and discussed

Jauny, G. Kumar · 0 citations
Open access Jul 2026

A Hybrid Conjugate Gradient Method for Unconstrained Optimization with Application in Image Restoration

Hybrid conjugate gradient methods are considered as an efficient family of conjugate gradient (CG) methods used to solve unconstrained optimization problems. In this paper, on account of the outstanding performance of the PRP (Polak–Ribière–Polyak) conjugate gradient method and its exceptional numerical computational stability, we propose a hybrid conjugate gradient method for solving unconstrained optimization problems. By combining two PRP-type directions via convex combination, the proposed search direction dynamically adjusts to gradient change rates and satisfies the sufficient descent property. Under mild conditions, the global convergence of the proposed method is established. Numerical computations are presented to display the efficacy of the proposed algorithm compared to some existing algorithms. It is indicated that the proposed method is more effective in dealing with non-convex optimization problems. Finally, the applicability of the proposed method is shown in image restoration problems with noise, and preliminary experimental results demonstrate its effectiveness compared to some other methods.

Jiayu Zheng, Xiangsong Zhang · 0 citations
Preprint Jul 2026

Fully Convergent Projection-based Methods with Momentum under Nonconvex Geometric

This work can specifically ensure, without any smoothness assumptions, convergence to Mordukhovich stationarity as long as the base directions asymptotically revert to the negative gradient for small stepsizes.

Matteo Lapucci, Diego Scuppa · 0 citations
Preprint Aug 2026

A proximal gradient method with adaptive backtracking for weakly smooth multiobjective optimization

In this paper, we propose a proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have H\"older continuous gradients. The proposed method is parameter-free as we do not require prior knowledge of parameters related to the weak smoothness of the objective function; the proposed linesearch finds an appropriate step-size that adapts to the weak smoothness. The complexity guarantee analyzed in this paper for the non-convex case is compatible with related works and our algorithm accepts coercer stationarity measure compared to existing methods. We also establish a novel complexity result for the convex case which improves the one in non-convex case.

Yuki Miyazaki, Masaru Ito, Shotaro Yagishita · 0 citations

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