Aug 2026· Reserche operationelle· Vol 60, pp. 2771-2786· 0 citations· 13 references
Abstract
As an extension of convex quadratic optimization (CQO) problems, the weighted convex quadratic optimization (WCQO) plays an important role in the domain of mathematical programming and engineering. In this paper, we propose a short-step primal-dual interior-point algorithm for solving WCQO based on the strategy of weighted-path. The latter generates only full-Newton steps and requires no line search. Under appropriate conditions, the algorithm converges locally quadratically to an optimal solution of WCQO. Moreover, it has the best well-known polynomial complexity, namely, O(√n log(n/ϵ)).
Finally, some numerical results are reported to confirm the efficiency of our proposed algorithm.
A new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian that achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual, the first second-order method for this problem class attaining this rate.
For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this pa...
F. Curtis, Ling-Jun Guo, Daniel P. Robinson· 0 citations
This work considers a quadratic minmax problem with coupled inner constraints and proposes a method to compute a class of stationary points and shows in particular that the method is polynomial in the special case where the inner feasible set of the authors' constrained minmax problem is independent from outer variable...
Stefano Cipolla, O. Stein, Alain B. Zemkoho· 1 citation
The method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when both the function and constraints are deterministic, when the function is stochastic and the constraints are deterministic, and when both are stochastic.
Theoretical analysis confirms that these inexact variants of GRPDA retain the convergence properties of their exact counterparts, and they are applied to some total-variation-based image deblurring problems.
