Comments on “A Note on the Paper “Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors””

Journal of Optimization Theory and Applications - Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012)....     

SYNTHESIS OF SPIRO [1,3-BENZODIOXOLE-2,4′-(3′H) QUINAZOLINES]

Abstract

In the present investigation, the authors could obtain a new series of spiranes (1) through the reaction of the high potential quinone tetrachloro-o-benzoquinone with 2-aryl-3-phenyl-3H-quinazoline-4-thiones. Thus, 2,3-diphenyl- (2a), 2-p-tolyl-3-phenyl- (2b) and 2-p-anisyl-3-phenyl- (2c)-3H-quinazoline-4-thiones react readily with tetrachloro-o-benzoquinone, in boiling toluene, to give the corresponding spiro-1,3-benzodioxole-2,4′-(3′H)-quinazolines (1a-c), respectively.     

Essential Oils Derived from Cistus Species Activate Mitochondria by Inducing SIRT1 Expression in Human Keratinocytes,Leading to Senescence Inhibition

Cistus L. is a genus of dicotyledonous perennial herbaceous plants. Cistus species have been commonly used in folk medicine in the Mediterranean region. In the present study, the biological activities of essential oils derived from Cistus species (Cistus laurifolius, C. monspeliensis, C. creticus, and C. salviifolius) were evaluated. Essential oils derived from C. laurifolius and C. monspeliensis were found to augment the expression of SIRT1, an anti-aging gene, in the normal culture of HaCaT cells. Furthermore, these essential oils increased the number and size of mitochondria and augmented their activity. These effects were thought to be caused by the up- and downregulated expression of MITOL and Drp1 in HaCaT cells, respectively, in response to the essential oil treatment. In addition, these essential oils were found to attenuate ultraviolet-B-induced mitochondrial damage and cellular senescence in HaCaT cells. These findings indicate that essential oils derived from C. laurifolius and C. monspeliensis may inhibit skin aging through mitochondrial regulation via SIRT1 activation.     

Lie algebras and separable morphisms in pro-affine algebraic groups

Let be an algebraically closed field of arbitrary characteristic, and let be a surjective morphism of connected pro-affine algebraic groups over . We show that if is bijective and separable, then is an isomorphism of pro-affine algebraic groups. Moreover, is separable if and only if (its differential) is surjective. Furthermore, if is separable, then .

     

On the Regularity Condition for Vector Programming Problems

In this work, we use a notion of approximation derived from Jourani and Thibault [13] to ascertain optimality conditions analogous to those that established but applicable to larger class of vector valued objective mappings and constraint set-valued mappings. To this end, we introduce an appropriate regularity condition to help us discern the Karush-Kuhn-Tucker multipliers.     

Adaptive Diagnosis for Fault Tolerant Data Fusion Based on α-Rényi Divergence Strategy for Vehicle Localization

When applying a diagnostic technique to complex systems, whose dynamics, constraints, and environment evolve over time, being able to re-evaluate the residuals that are capable of detecting defaults and proposing the most appropriate ones can quickly prove to make sense. For this purpose, the concept of adaptive diagnosis is introduced. In this work, the contributions of information theory are investigated in order to propose a Fault-Tolerant multi-sensor data fusion framework. This work is part of studies proposing an architecture combining a stochastic filter for state estimation with a diagnostic layer with the aim of proposing a safe and accurate state estimation from potentially inconsistent or erroneous sensors measurements. From the design of the residuals, using α-Rényi Divergence (α-RD), to the optimization of the decision threshold, through the establishment of a function that is dedicated to the choice of α at each moment, we detail each step of the proposed automated decision-support framework. We also dwell on: (1) the consequences of the degree of freedom provided by this α parameter and on (2) the application-dictated policy to design the α tuning function playing on the overall performance of the system (detection rate, false alarms, and missed detection rates). Finally, we present a real application case on which this framework has been tested. The problem of multi-sensor localization, integrating sensors whose operating range is variable according to the environment crossed, is a case study to illustrate the contributions of such an approach and show the performance.     

Necessary optimality conditions for bilevel set optimization problems

Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.      

Optimality Conditions for D.C. Vector Optimization Problems Under Reverse Convex Constraints

In this paper, we establish global necessary and sufficient optimality conditions for D.C. vector optimization problems under reverse convex constraints. An application to vector fractional mathematical programming is also given. Mathematics Subject Classifications (1991). Primary 90C29, Secondary 49K30.     

Second order optimality conditions for bilevel set optimization problems

In this paper, we introduce a new notion of augmenting function known as indicator augmenting function to establish a minmax type duality relation, existence of a path of solution converging to optimal value and a zero duality gap relation for a nonconvex primal problem and the corresponding Lagrangian dual problem. We also obtain necessary and sufficient conditions for an exact penalty representation in the framework of indicator augmented Lagrangian.