In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

We present polarimetric maps of the Circinus galaxy nucleus in $BVRI$ bands, obtained with VLT/FORS2. is closest Seyfert 2 and harbours an archetypal obscured active galactic (AGN). Recent high angular resolution imaging revealed that a major fraction its mid-infrared (MIR) emission coming from polar region. Previously, we demonstrated these observations are consistent model compact dusty disc ...

A surface geometric constraint approach is used in designing the trajectories of a solar sail. We solve sail equation motion by obtaining generalized Laplace-Runge-Lenz (LRL) vector with assumption that cone angle constant throughout mission. family trajectory solutions can then be specified defining relates radial velocity to polar spacecraft. The method generate and analyze are constrained on...

Inspired by the connection between ovoids and unitals arising from Buekenhout construction in André/Bruck-Bose representation of translation planes dimension at most two over their kernel, since eggs $$\textrm{PG}(4m-1,q)$$ , $$m\ge 1$$ are a generalization ovoids, we explore relation higher kernel. By investigating such relationship, construct unital Dickson semifield plane order $$3^{10}$$ wh...

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible to develop very efficient optimization met...

We consider a primal-dual short-step interior-point method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the primal and dual barrier functions is either impossible or prohibitively expensive. As our main contribution, we show that if approximate gradients and Hessians of the primal barrier function can be computed, and the relative errors in su...

The minimum principle of complementary energy is established for cable networks involving only stress components as variables in geometrically nonlinear elasticity theory. The stress-strain relation is assumed to be piecewise linear. It is rather amazing that the complementary energy always attains minimum value at the equilibrium state irrespective of the stability of cable networks, contrary ...