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981.
《Optimization》2012,61(10):2111-2129
In this paper, the constraints of the sequential optimization of the lexicographic approach are relaxed in order to obtain a simple alternative approach to solve multiobjective problems. In other words, we allow the decision-maker to deviate from the optimal solution of each iteration if he/she prefers. Some properties of the obtained solutions are studied and the relationship between these solutions and those of the weighted sum scalarization and the ?-constraint scalarization and also the elastic ?-constraint scalarization are investigated. Finally, some examples are provided to show more details. 相似文献
982.
《Optimization》2012,61(6):1187-1201
ABSTRACTSeveral optimization problems of modifying the weight of vertices in rooted trees, some of which are special cases of the inverse 1-median problem, are solved. Such problems arise in Very Large Scale Integration (VLSI) design of hardware security circuits, circuit synchronization, and analog-to-digital converters. These problems require assigning costly hardware (demands) to the leaves of rooted trees. One common property of these problems is that a resource allocated to an internal node can be shared by the entire sub-tree emanated at the node. Two types of problems are studied here. (1) A tree node employs an addition operation and the demands at the leaves are obtained by summing the resources allocated to nodes along the root-to-leaf paths. A linear-time bottom-up algorithm is shown to minimize the total resources allocated to tree nodes. (2) A tree’s node employs a multiplication operation and the demands at the leaves are obtained by multiplying the resources allocated to nodes along the root-to-leaf paths. A bottom-up dynamic programming algorithm is shown to minimize the total resources allocated to the tree’s nodes. While the above problems are usually solved by design engineers heuristically, this paper offers optimal solutions that can be easily programmed in CAD tools. 相似文献
983.
In this article,the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established.This contributes to certain recent results obtained by Y.Wei [9]. 相似文献
984.
Takashi Takiguchi 《数学物理学报(B辑英文版)》2012,(4):1637-1646
We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem. 相似文献
985.
胡国恩 《数学物理学报(B辑英文版)》2012,(4):1529-1544
In this paper, some weighted estimates with general weights are established for the m-linear Caldern-Zygmund operator and the corresponding maximal operator. It is proved that, if p1 , ··· , pm ∈ [1, ∞] and p ∈ (0, ∞) with 1/p = ∑m k=1 1/pk , then for any weight w, integer ■with 1 ≤■≤ m, these operators are bounded from L p 1 (Rn , MBw) ×···× Lp■(Rn , MBw) × Lp +1 (Rn , Mw) ×···× Lp m (Rn , Mw) to Lp, ∞ (R n , w) or L p (R n , w), where B is a Young function and M B is the maximal operator associated with B. 相似文献
986.
In the present paper we consider a time-fractional inverse diffusion problem, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is typically ill-posed: the solution (if it exists) does not depend continuously on the data. We give a new iteration regularization method to deal with this problem, and error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Furthermore, numerical implement shows the proposed method works effectively. 相似文献
987.
The aim of this study is to develop new linguistic aggregation operators based on the power-average (PA) operator, such as the linguistic power average (LPA) operator, the linguistic weighted PA operator, and the LPOWA operator. We studied some desired properties of the developed operators, such as idempotency and commutativity. Moreover, we developed two approaches to deal with group decision-making problems under linguistic environments. If the weighting vector of the decision makers was known, we developed an approach based on the linguistic weighted PA operator. On the other hand, if the weighting vector of the decision maker was unknown, we developed a different approach based on the LPOWA operator. We also developed new uncertain linguistic operators under uncertain linguistic environments, such as the ULPA operator, the uncertain linguistic weighted PA operator, and the ULPOWA operator. We extended these approaches, which are based on ULWPA and ULPOWA operators, respectively, to solve group decision-making problems under an uncertain linguistic environment. Finally, a practical example is provided to illustrate the multiple-attribute group decision-making process. 相似文献
988.
989.
1引 言与引理
最近,文[1]定义了长方矩阵的一种加权群逆:设A∈Cm×n,W∈Cn×m.称满足下列矩阵方程组的矩阵X∈Cm×n为A的加W权群逆:(W1)AWXWA=A, (W2)XWAWX=X, (W3)AWX=XWA通常记A的加W权群逆为A#W.若A#W存在,则它是唯一的. 相似文献
990.