In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints are derived under the Mangasarian-Fromovitz condition and under the assumption that the state and control constraint functions are smooth. In this paper we d...

This paper investigates the problem concerning the existence of a solution to a diverse class of optimal allocation problems which include models of cake eating, exhaustible resource extraction, life-cycle saving, and nonatomic games. A new formulation that encompasses all these diverse models is provided. Examples of these models for which a solution does not exist and the causes of the non-ex...

We develop necessary conditions of broad applicability for optimal control problems in which the state and control are subject to mixed constraints. We unify, subsume and significantly extend most of the results on this subject, notably in the three special cases that comprise the bulk of the literature: calculus of variations, differential-algebraic systems, and mixed constraints specified by ...

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. Existence and uniqueness of the plastic multiplier is rigorously proved, which allows for the re-formulation of the forward system using a complementarity condition. I...

the opuntia ficus indica mucilage was an abundant and a low cost product. in the presentpaper, it was tested as an eco-friendly flocculants for textile waste water treatment. its performance asflocculants in decolorization, cod removal and turbidity abatement was checked. the natural product wascharacterized using uv-vis and infra-red spectroscopy. the study of the effect, followed by an optimi...

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Camoptimality theory is adapted to cover this situation.We show that the expect...

Different methods based on photogrammetry or self-calibration exist to calibrate intrinsic and extrinsic camera parameters and also for data pre- and post-processing. From a practical viewpoint, it is quite difficult to decide which calibration method gives accurate results and even whether any data processing is necessary. This paper proposes a set of optimal conditions to resolve the calibrat...

The aim of this study was production and partial purification of α-amylase enzyme by Bacillus licheniformis. B. Licheniformis was allowed to grow in broth culture for purpose of inducing α-amylase enzyme. Optimal conditions for amylase production by B. Licheniformis are incubation period of 120 h, temperature of 37 °C and pH 7.0. The α-amylase enzyme was purified by ion exchange chromatography ...