Optimality conditions for pareto nonsmooth nonconvex programming in banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush-Kuhn-Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

On the proximal Landweber Newton method for a class of nonsmooth convex problems

We consider a class of nonsmooth convex optimization problems where the objective function is a convex differentiable function regularized by the sum of the group reproducing kernel norm and (Formula presented.)-norm of the problem variables. This class of problems has many applications in variable selections such as the group LASSO and sparse group LASSO. In this paper, we propose a proximal Landweber Newton method for this class of convex optimization problems, and carry out the convergence and computational complexity analysis for this method. Theoretical analysis and numerical results show that the proposed algorithm is promising.

The generation of virtual prototypes for performance optimization

I am suspicious of tools without a purpose - tools that are not developed in response to a clearly defined problem. Of course tools without a purpose can still be useful. However the development of first generation CAD was seriously impeded because the solution came before the problem. We are in danger of repeating this mistake if we do not clarify the nature of the problem that we are trying to solve with the next generation of tools. Back in the 1980s I used to add a postscript slide at the end of CAD conference presentations and the applause would invariably turn to concern. The slide simple asked: can anyone remember what it was about design that needed aiding before we had computer aided design?

Heavy truck suspension optimization based on modified skyhook damping control

This paper presents a multi-objective optimization strategy for heavy truck suspension systems based on modified skyhook damping (MSD) control, which improves ride comfort and road-friendliness simultaneously. A four-axle heavy truck-road coupling system model was established using functional virtual prototype technology; the model was then validated through a ride comfort test. As the mechanical properties and time lag of dampers were taken into account, MSD control of active and semi-active dampers was implemented using Matlab/Simulink. Through co-simulations with Adams and Matlab, the effects of passive, semi-active MSD control, and active MSD control were analyzed and compared; thus, control parameters which afforded the best integrated performance were chosen. Simulation results indicated that MSD control improves a truck’s ride comfort and roadfriendliness, while the semi-active MSD control damper obtains road-friendliness comparable to the active MSD control damper.

Constraints on the complete optimization of human motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.

A cost-based optimization of a fiberboard pressing plant using Monte-Carlo simulation (a reliability program)

In this research the reliability and availability of fiberboard pressing plant is assessed and a cost-based optimization of the system using the Monte- Carlo simulation method is performed. The woodchip and pulp or engineered wood industry in Australia and around the world is a lucrative industry. One such industry is hardboard. The pressing system is the main system, as it converts the wet pulp to fiberboard. The assessment identified the pressing system has the highest downtime throughout the plant plus it represents the bottleneck in the process. A survey in the late nineties revealed there are over one thousand plants around the world, with the pressing system being a common system among these plants. No work has been done to assess or estimate the reliability of such a pressing system; therefore this assessment can be used for assessing any plant of this type.