We introduce two derivative-free spectral projection methods for large-scale monotone equations with convex constraints. The first, SOPP (Spectral Optimal-Perry Projection), selects its Perry parameter by minimizing the condition number of a symmetrized Perry matrix over its positive definite range, in place of the eigenvalue-gap criterion used in earlier work. A clipping step gives its search direction a trust-region property by construction. The second, SDLP (Spectral Dai–Liao Projection), replaces a fixed Dai–Liao factor with an adaptive spectral parameter. Both directions satisfy sufficient descent independently of the line search. Under standard assumptions each method either terminates finitely at a solution or generates a whole sequence converging to one. The SOPP result requires no Lipschitz continuity, whereas the SDLP analysis does. Numerical experiments on benchmark problems and two applications indicate that both methods are computationally viable and stable under reasonable parameter choices.
A hyperbolic-majorization preconditioned three-term nonlinear conjugate-gradient framework for nonconvex finite minimax optimization that yields a Dai--Liao-type conjugacy relation, enhanced sufficient descent, a smoothing-parameter-uniform Armijo lower bound, fixed-smoothing global first-order convergence and complexi...
The forward-reflected-backward (FRB) splitting solves inclusion problems involving the sum of a maximally monotone operator and a monotone Lipschitz continuous operator. Each iteration performs one resolvent step and one evaluation of the Lipschitz operator, plus a reflection term with coefficient one that reuses the p...
Hong-Jia Ou, Andreas Themelis, Puya Latafat· 0 citations
Four groups of subspace methods for nonlinear monotone equations, with applications to large-scale machine learning problems, using Jacobian-free subspace directions of conjugate-gradient type combined with either fixed step sizes or variable step sizes generated by the projected method of Solodov and Svaiter are intro...
M. Kimiaei, Shima Shabani, Michael Breuß· 0 citations
The results show that the proposed Wolfe-type spectral conjugate gradient 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.
We study nonsmooth convex-concave saddle-point problems over compact convex sets, assuming access to stochastic subgradients of the payoff function. We develop single-loop projection-free algorithms that use linear minimization oracles over the primal and dual domains. Unlike prior projection-free approaches that rely...
