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71.
P. A. V. Ferreira M. E. S. Machado 《Journal of Optimization Theory and Applications》1996,89(3):659-680
Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNPq and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments. 相似文献
72.
证明如下结果,设X是Banach空间,则X是无限维的充分必要的条件是存在不含内点的非空凸集B,使得B不在任何一个闭超平面上。 相似文献
73.
Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x
n)}, where {x
n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper. 相似文献
74.
Mordechai I. Henig 《Mathematical Programming》1990,46(1-3):205-217
In the absence of a clear objective value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications potential optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions. 相似文献
75.
Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r
q
, whereq depends on the properties of the norm. We specify it in the case ofL
spaces, >1. 相似文献
76.
Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG()
D
. The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably. 相似文献
77.
Convex programs with an additional reverse convex constraint 总被引:2,自引:0,他引:2
H. Tuy 《Journal of Optimization Theory and Applications》1987,52(3):463-486
A method is presented for solving a class of global optimization problems of the form (P): minimizef(x), subject toxD,g(x)0, whereD is a closed convex subset ofR
n
andf,g are convex finite functionsR
n
. Under suitable stability hypotheses, it is shown that a feasible point
is optimal if and only if 0=max{g(x):xD,f(x)f(
)}. On the basis of this optimality criterion, the problem is reduced to a sequence of subproblemsQ
k
,k=1, 2, ..., each of which consists in maximizing the convex functiong(x) over some polyhedronS
k
. The method is similar to the outer approximation method for maximizing a convex function over a compact convex set. 相似文献
78.
J. -B. Hiriart-Urruty 《Journal of Optimization Theory and Applications》1986,48(1):127-140
Given a convex functionf:
p
×
q
(–, +], the marginal function is defined on
p
by (x)=inf{f(x, y)|y
q
}. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx
0 in terms of those off at (x
0,y
0), wherey
0 is any element for which (x
0)=f(x
0,y
0).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1. 相似文献
79.
The nano-ZnFe2O4/TiO2 films possess the functions of desulfurization and degradation for organic pollutants. The sols of ZnFe2O4/TiO2 were prepared by sol-gel method and coated on glass and porous ceramic by vertical coating and dipping-lift processes, respectively, and the samples were obtained after drying and sintering. The composition, appearance, absorption spectrum of the films, and the influence of the film on porous ceramic performances were analyzed using SEM, AFM, UV-Vis spectrometer, and mercury porosimeter, respectively, to determine the operation parameters of the multifunction porous ceramic elements for gas-purification. 相似文献
80.
Muhammad Adil Khan Shahid Khan Samet Erden Muhammad Samraiz 《Mathematical Methods in the Applied Sciences》2022,45(1):36-48
There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory. 相似文献