Embedding approaches can be used for solving non linear programs \emph{P}. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to \emph{P}. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on \emph{P}. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence are fulfilled under very restrictive hypothesis. In this paper, we present a new multipliers embedding such that the objective function and the constraints of P(t) are C3 differentiable functions. We prove that the parametric problem satisfies the \emph{JJT}-regularity generically, a necessary condition for the success of the path-following method.
Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of $E$, thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.
The cubical dimension of a graph $G$ is the smallest dimension of a hypercube into which $G$ is embeddable as a subgraph. The conjecture of Havel (1984) claims that the cubical dimension of every balanced binary tree with $2^n$ vertices, $n\geq 1$, is $n$. The 2-rooted complete binary tree of depth $n$ is obtained from two copies of the complete binary tree of depth $n$ by adding an edge linking their respective roots. In this paper, we determine the cubical dimension of trees obtained by subdividing twice a 2-rooted complete binary tree and prove that every such balanced tree satisfies the conjecture of Havel.
In this paper, characterizations of the embeddings between weighted Copson function spaces ${\rm Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Cesàro function spaces ${\rm Ces}_{p_2,q_2}(u_2,v_2)$ are given. In particular, two-sided estimates of the optimal constant $c$ in the inequality $ \align\biggl( \int_0^{\infty} &\biggl( \int_0^t f(\tau)^{p_2}v_2(\tau)\dd\tau\biggr)^{\!\!\frc{q_2}{p_2}} u_2(t)\dd t\biggr)^{\!\!\frc1{q_2}} $ \ $\le c \biggl( \int_0^{\infty} \biggl( \int_t^{\infty} f(\tau)^{p_1} v_1(\tau)\dd\tau\biggr)^{\!\!\frc{q_1}{p_1}} u_1(t)\dd t\biggr)^{\!\!\frc1{q_1}}, $ where $p_1,p_2,q_1,q_2 \in(0,\infty)$, $p_2 \le q_2$ and $u_1,u_2,v_1,v_2$ are weights on $(0,\infty)$, are obtained. The most innovative part consists of the fact that possibly different parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$ and $v_2$ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities., Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver., and Obsahuje bibliografii
A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.
In this paper we apply the notion of the product $MV$-algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an $MV$-algebra into a product $MV$-algebra. We found sufficient conditions under which any two direct product decompositions of a product $MV$-algebra have isomorphic refinements.
Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.