Optimality conditions in terms of Bouligand generalized differentials for a nonsmooth semilinear elliptic optimal control problem with distributed and boundary control pointwise constraints

We prove a novel optimality condition in terms of Bouligand generalized differentials for a local minimizer of optimal control problems governed by a nonsmooth semilinear elliptic partial differential equation with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient in the state equation is not differentiable at one point. Therefore, the Bouligand subdifferential of this nonsmooth coefficient in every point consists of one or two elements that will be used to construct the two associated Bouligand generalized derivatives of the control-to-state operator in any admissible control. We also establish the optimality conditions in the form of multiplier existence. There, in addition to the existence of the adjoint state and of the nonnegative multipliers associated with the pointwise constraints as usual, other nonnegative multipliers exist and correspond to the nondifferentiability of the control-to-state mapping. The latter type of optimality conditions shall be applied to the optimal control problems without distributed and boundary pointwise constraints to derive the so-called \emph{strong} stationarity conditions, where the sign of the associated adjoint state does not vary on the level set of the corresponding optimal state at the value of nondifferentiability.Comment: 33 page

Optimization of technological parameters in ultrasonic welding of the polypropylene fabric using Taguchi and FCCCD methods

Ultrasonic welding is a welding method that has been applied for welding nonwoven fabrics, with many advantages such as fast speed, high reliability, easy automation and especially less pollution to the environment. This paper studies the optimization of technological parameters in the welding process such as welding time, pressure, and weld shape on the breaking strength of ultrasonic welding of Polypropylene (PP) nonwovens. To evaluate the influence level and find the reasonable technological parameters domain in the paper, the Taguchi method is used in combination with the face-centered central composite design (FCCCD) response surface method. The research results have determined the regression equations used to calculate the breaking strength for each weld shape as well as the optimal domain for the main technological parameters, ensuring the breaking strength of the weld. There are different degrees of influence of technological parameters (shape of the weld zone, welding time and welding pressure) on the breaking strength of ultrasonic welds. Among them, the influence level of welding time t is 45.31 %, the weld shape is Pattern 2 with the rate of 30.03 %, and the welding pressure is 24.66 %. Carrying out a verification test with the welding parameters: t=1.6 s, p=3.1 kgf/cm2, two patterns ( Pattern 2 and Pattern 3), the result of breaking strength for patterns was achieved. Pattern 2 has a difference of 1.19 % between the regression equation results and the actual experimental results, while the figure for Pattern 3 is 0.77 %. From these results, it is possible to select the appropriate technological parameters for ultrasonic welding equipment when processing products from nonwoven fabrics to ensure the highest quality and productivit

STUDY ON APPLICABILITY OF THE CONTACT OXIDATION PROCESS IN REMOVAL OF ORGANIC POLLUTANTS FROM TEXTILE WASTEWATER

Joint Research on Environmental Science and Technology for the Eart