نتایج جستجو برای: generalized n set convex function

تعداد نتایج: 2717715  

Journal: :Information & Computation 2021

In the generalized budgeted submodular set function maximization problem, we are given a ground of elements and bins. Each bin has its own cost each element depends on associated bin. The goal is to find subset along with an bins such that overall costs both at most budget, profit maximized. We present algorithm guarantees 12(1?1e?)-approximation, where ??1 approximation factor for sub-problem....

Journal: :bulletin of the iranian mathematical society 2015
m. darus i. aldawish r. w. ibrahim

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.

Journal: :Journal of Global Optimization 2021

This paper focuses on second-order necessary optimality conditions for constrained optimization problems Banach spaces. For in the classical setting, where objective function is $$C^2$$ -smooth, we show that strengthened are valid if constraint set generalized polyhedral convex. a new just assumed to be $$C^1$$ -smooth and convex, establish sharp based Fréchet subdifferential of tangent set. Th...

2003

We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in m×n , min(m,n) 6 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit conve...

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

B. Bagaban D. Sashi Bhusan J.P. Tripathy,

The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...

1996
Defeng Sun Masao Fukushima Liqun Qi

It is known that the variational inequality problem (VIP) can be converted to a differentiable unconstrained optimization problem via a merit function first considered by Peng and later studied further by Yamashita, Taji and Fukushima. This merit function, called the D-gap function, though is differentiable, is not twice differentiable and its generalized Hessian with existing definitions is ve...

2008
Libor Veselý

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K aF is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the fi...

Journal: :Discrete Mathematics 1996
John L. Pfaltz

Closure spaces have been previously investigated by Paul Edelman and Robert Jami-son as \convex geometries". Consequently, a number of the results given here duplicate theirs. However, we employ a slightly diierent, but equivalent, deening axiom which gives a new avor to our presentation. The major contribution is the deenition of a partial order on all subsets, not just closed (or convex) subs...

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