arXiv:2607. 08954v1 Announce Type: cross Abstract: We study nonasymptotic convergence of primal-dual methods for a class of nonconvex constrained optimization problems with a convex-composite structure.
arXiv:2608. 12665v1 Announce Type: cross Abstract: For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
arXiv:2608. 05502v1 Announce Type: cross Abstract: In this paper, we consider a class of multiblock nonconvex nonsmooth optimization problems, which covers many applications such as the analysis of pre-earthquake anomalies and machine learning.
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.
The paper introduces AutoConvexRelax, a learning-based framework that automates the design of convex relaxations for nonconvex optimization problems. By representing a problem as a tripartite graph of variables, symbolic terms, and objective/constraint positions, the method learns a policy to compose symbolic rewrites that generate valid relaxation trajectories. Experiments on quadratic and fractional problems show that the learned policy improves McCormick lower bounds by 13.52% and achieves near‑semidefinite bounds while using smaller formulations.
arXiv:2610. 13787v1 Announce Type: cross Abstract: We present new algorithms for stochastic optimization problems in which the objective is neither smooth nor convex, subject to a convex constraint set.
arXiv:2608. 21359v1 Announce Type: cross Abstract: We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian.
The paper introduces the Generalized Geometry Block Proximal Linearized (GGBPL) method, which uses a generalized geometry proximal linearized operator to update block variables in multiblock nonconvex and nonsmooth optimization problems. By allowing arbitrary inner products and admissible metrics, GGBPL adapts to the geometric structure of various problems, improving numerical efficiency over traditional Euclidean‑based methods. An inertial variant (iGGBPL) is also presented, and a unified convergence framework is established, proving objective convergence, global convergence to a critical point, and an ε‑stationary point iteration complexity of φ(ε−−). The methods are applied to sparse nonnegative matrix factorization and sparse nonnegative CP decomposition with λ₀ constraints, showing superior performance in numerical experiments.
arXiv:2504.09409v3 Announce Type: replace-cross Abstract: In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective e...
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.