Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given

Personalized Federated Learning via ADMM with Moreau Envelope

Personalized federated learning (PFL) is an approach proposed to address the issue of poor convergence on heterogeneous data. However, most existing PFL frameworks require strong assumptions for convergence. In this paper, we propose an alternating direction method of multipliers (ADMM) for training PFL models with Moreau envelope (FLAME), which achieves a sublinear convergence rate, relying on the relatively weak assumption of gradient Lipschitz continuity. Moreover, due to the gradient-free nature of ADMM, FLAME alleviates the need for hyperparameter tuning, particularly in avoiding the adjustment of the learning rate when training the global model. In addition, we propose a biased client selection strategy to expedite the convergence of training of PFL models. Our theoretical analysis establishes the global convergence under both unbiased and biased client selection strategies. Our experiments validate that FLAME, when trained on heterogeneous data, outperforms state-of-the-art methods in terms of model performance. Regarding communication efficiency, it exhibits an average speedup of 3.75x compared to the baselines. Furthermore, experimental results validate that the biased client selection strategy speeds up the convergence of both personalized and global models.Comment: 15 page

Research on Design Method of Long-life Asphalt Pavement

In recent years, the problem of early damage of asphalt pavement has been basically solved, and the service performance has been improved, but there are still some deficiencies in design life and service life. This paper investigates the long-life asphalt pavement structure, analyzes the design method of asphalt mixture, and summarizes the pavement design theory and related software. The long-life asphalt pavement with semi-rigid base, flexible base and combined base structure has been designed by four method, including typical load, Per-Road, D50-2006 and D50-2017. Four methods were compared by designing long-life pavements with semi-rigid base and flexible base. The results show that the proposed asphalt pavement structure can meet the requirements of Per-Road, typical load design and D50-2006. However, D50-2017 has higher requirements for the bending and tensile fatigue life of the base layer and requires a thicker base layer. When d50-2017 is used to design flexible base pavement, the fatigue life of asphalt layer should be the main control index, and the fatigue life of sub base course should be the main control index in other pavement de-sign. It remains to be seen whether the proposed highway structure can achieve the design goal of long-life asphalt pavement

Research on Design Method of Long-life Asphalt Pavement

In recent years, the problem of early damage of asphalt pavement has been basically solved, and the service performance has been improved, but there are still some deficiencies in design life and service life. This paper investigates the long-life asphalt pavement structure, analyzes the design method of asphalt mixture, and summarizes the pavement design theory and related software. The long-life asphalt pavement with semi-rigid base, flexible base and combined base structure has been designed by four method, including typical load, Per-Road, D50-2006 and D50-2017. Four methods were compared by designing long-life pavements with semi-rigid base and flexible base. The results show that the proposed asphalt pavement structure can meet the requirements of Per-Road, typical load design and D50-2006. However, D50-2017 has higher requirements for the bending and tensile fatigue life of the base layer and requires a thicker base layer. When d50-2017 is used to design flexible base pavement, the fatigue life of asphalt layer should be the main control index, and the fatigue life of sub base course should be the main control index in other pavement de-sign. It remains to be seen whether the proposed highway structure can achieve the design goal of long-life asphalt pavement

Modified generalised successive over-relaxation method for augmented linear systems

We introduce here a modified generalised successive over-relaxation (MGSOR) method to solve augmented linear systems. We prove that the MGSOR method converges to the unique solution of the linear system for a loose restriction on three parameters. Finally, a numerical example illustrates the effectiveness of the MGSOR iteration method which outperforms the modified SOR-like method and the generalised successive over-relaxation method. References Z. Z. Bai, B. N. Parlett, Z. Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math., 102(2005), 1--38, doi:10.1007/s00211-005-0643-0 G. H. Golub, X. Wu, J. Y. Yuan, SOR-like methods for augmented systems, BIT, 41(2001), 71--85, doi:10.1023/A:1021965717530 X. H. Shao, Z. Li, C. J. Li, Modified SOR-like method for the augmented system, Int. J. Comput. Math., 84(2007), 1653--1662, doi:10.1080/00207160601117313 F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer--Verlag, New York and London, 1991. M. Fortin, R. Glowinski, Augmented Lagrangian Methods, Applications to the Numerical Solution of Boundary Value Problems, North--Holland, Amsterdam, 1983. M. T. Darvishi, P. Hessari, Symmetric SOR method for augmented systems, Appl. Math. Comput., 183(2006), 409--415, doi:10.1016/j.amc.2006.05.094 D. M. Young, Iterative Solution for Large Linear Systems, Academic Press, New York, 1971

Self-Healing Properties of Water Tree with Microcapsule/Cross-Linked Polyethylene Composite Material Based on Three-Layer Core-Shell Structure

To overcome the degradation of insulating properties caused by the water tree aging of cross-linked polyethylene (XLPE), a self-repairing material for XLPE based on a microcapsule system is proposed. Three-layer shell nucleus microcapsules/XLPE composites with different microcapsule doping content are prepared. The water tree aging experiments are carried out using the water-needle electrode method to analyze the ability of microcapsules to repair the damaged areas of water trees. The results show that, compared with the XLPE material without microcapsules, the electrical properties of composites decline significantly when the doping concentration of three-layer shell nucleus microcapsules is large. When the doping concentration is 1.0 wt%, the microcapsule/XLPE composite breakdown strength has no noticeable change, and the dielectric loss factor does not change significantly, the space charge density decreases, and the space charge properties have been improved considerably. When the water tree branch develops to the position where the microcapsules are located, the microcapsules will rupture and release their internal repair materials and catalysts and react with water to produce an organic silicone resin to fill the water tree cavity, which can achieve an excellent self-healing effect. In addition, the nano-SiO2 on the surface microcapsules can make the microcapsules and matrix better integrated, which avoids the microcapsule accumulation that tends to occur when incorporating microcapsules, thus improving the repair rate

Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case

The scalar \ufb01nite-dimensional case has been discussed in the \ufb01rst part of this work series, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. Based on this preliminary result, the present paper dedicates itself to further study the regularity conditions for vector constrained extremum problems in a Euclidean space. The case of in\ufb01nite-dimensional image will be the subject of a subsequent paper