Complexity analysis and numerical implementation of primal-dual interior-point methods for convex quadratic optimization based on a finite barrier

Design and analysis of recurrent neural network models with non‐linear activation functions for solving time‐varying quadratic programming problems

“…In Figure 1c, in addition to the ZNN model [24], the residual errors of ZNN models are able to converge to zero within 3 s, substantiating the properties of finite-time convergent previously proved. Moreover, it is revealed in Figure 1c that proposed SSZNN models (12) and CZNN models (14) converge faster than the traditional SBPZNN model (6), with the CZNN model (14) being the fastest, which is also consistent with the previous theorems and reflects the superiority of the new models. Furthermore, comparisons among these diverse models are summarised in Table 1.…”

“…In order to deal with such problems, numerous target approaches are put forward, most of which require numerical calculations. However, the complexity and costs of numerically solving QP problems are rather high, which is proportional to the cube of the dimension of its associated Hessian matrix [11][12][13]. Therefore, when dealing with relatively complex problems, most Xiaoyan Zhang and Liangming Chen are co-first authors and they are graduate students.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.…”

Implementation of Infeasible Kernel-Based Interior-Point Methods for Linearly Constrained Convex Optimization

“…Since the second condition is much simpler to check than the fifth condition, in many cases it is easy to know that () t  is eligible if it satisfies the first four conditions. Some wellknown eligible kernel functions are presented below (see, e.g., [2,3]). (1/ 1)…”

“…Yu et al [9] considered a polynomial predictor-corrector interior-point algorithm for CQO. Cai et al [3] proposed a class of primal-dual interior-point algorithms for CQO based on a finite barrier and obtained the currently best known iteration bound for large-and small-update methods.…”

A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization

“…Many interior-point methods (IPMs) for linear optimization (LO) are successfully extended to (SDO) due to their polynomial complexity and practical efficiency. For an overview of these results, we refer to [1,2] and the references [3,4,5,6,7,8,9,10,11,12,13].…”