A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

This work focuses on the development of a super-penalty strategy based on the $$L^2$$ L 2 -projection of suitable coupling terms to achieve $$C^1$$ C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.

An Economic Penalty Scheme for Optimal Parking Lot Utilization with EV Charging Requirements

In the parking lots of public commercial areas, such as shopping malls, hospitals, and scenic spots, the parking spaces with electric vehicle (EV) charging facilities are often occupied by ordinary cars. How to regulate the parking order in the parking lot is a key issue in the operation and management of the parking facilities. In this paper, a method of assessing parking fees for vehicles parked at the charging facilities is proposed based on an economic penalty strategy, including fixed-penalty and dynamic-penalty strategies. First, a traffic flow model of the parking lot in public area is established. Then, a price and consumption model of parking fees and parking lot utilization is established, along with different penalty strategies. Finally, taking the parking lot of a shopping mall as an example, the penalty strategies are optimized through particle swarm optimization (PSO) algorithm. The simulation results show that the method proposed can help to improve the utilization of EV charging facilities in parking lots and guide the orderly parking and charging of EVs at the same time.