共查询到10条相似文献,搜索用时 93 毫秒
1.
I. Ginchev A. Guerraggio M. Rocca 《Journal of Optimization Theory and Applications》2009,143(1):87-105
The present paper studies the following constrained vector optimization problem: min
C
f(x), g(x)∈−K, h(x)=0, where f:ℝ
n
→ℝ
m
, g:ℝ
n
→ℝ
p
and h:ℝ
n
→ℝ
q
are locally Lipschitz functions and C⊂ℝ
m
, K⊂ℝ
p
are closed convex cones. In terms of the Dini set-valued directional derivative, first-order necessary and first-order sufficient
conditions are obtained for a point x
0 to be a w-minimizer (weakly efficient point) or an i-minimizer (isolated minimizer of order 1). It is shown that, under natural assumptions (given by a nonsmooth variant of the
implicit function theorem for the equality constraints), the obtained conditions improve some given by Clarke and Craven.
Further comparison is done with some recent results of Khanh, Tuan and of Jiiménez, Novo. 相似文献
2.
James V. Burke 《Mathematical Programming》1987,38(3):287-302
In convex composite NDO one studies the problem of minimizing functions of the formF:=h ○f whereh:ℝ
m
→ ℝ is a finite valued convex function andf:ℝ
n
→ ℝ
m
is continuously differentiable. This problem model has a wide range of application in mathematical programming since many
important problem classes can be cast within its framework, e.g. convex inclusions, minimax problems, and penalty methods
for constrained optimization. In the present work we extend the second order theory developed by A.D. Ioffe in [11, 12, 13]
for the case in whichh is sublinear, to arbitrary finite valued convex functionsh. Moreover, a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature. 相似文献
3.
A nonsmooth multiobjective optimization problem involving generalized (F, α, ρ, d)-type I function is considered. Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a
feasible point to be an efficient or properly efficient solution. Duality results are obtained for mixed type dual under the
aforesaid assumptions. 相似文献
4.
E. Miglierina E. Molho M. Rocca 《Journal of Optimization Theory and Applications》2008,138(3):479-496
In this work, we study the critical points of vector functions from ℝ
n
to ℝ
m
with n≥m, following the definition introduced by Smale in the context of vector optimization. The local monotonicity properties of
a vector function around a critical point which are invariant with respect to local coordinate changes are considered. We
propose a classification of critical points through the introduction of a generalized Morse index for a critical point, consisting
of a triplet of nonnegative integers. The proposed index is based on the sign of an appropriate invariant vector-valued second-order
differential. 相似文献
5.
In this paper we extend Reiland’s results for a nonlinear (single objective) optimization problem involving nonsmooth Lipschitz
functions to a nonlinear multiobjective optimization problem (MP) for ρ − (η, θ)-invex functions. The generalized form of the Kuhn–Tucker optimality theorem and the duality results are established for
(MP). 相似文献
6.
We develop explicit, piecewise-linear formulations of functions f(x):ℝ
n
↦ℝ, n≤3, that are defined on an orthogonal grid of vertex points. If mixed-integer linear optimization problems (MILPs) involving
multidimensional piecewise-linear functions can be easily and efficiently solved to global optimality, then non-analytic functions
can be used as an objective or constraint function for large optimization problems. Linear interpolation between fixed gridpoints
can also be used to approximate generic, nonlinear functions, allowing us to approximately solve problems using mixed-integer
linear optimization methods. Toward this end, we develop two different explicit formulations of piecewise-linear functions
and discuss the consequences of integrating the formulations into an optimization problem. 相似文献
7.
Xiao Ping Yuan 《数学学报(英文版)》2001,17(2):253-262
We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping
nonlinearity
, where a,b > 0, p(t) ∈C(ℝ/2πℤ) and φ : ℝ→ℝ is an unbounded function.
Supported by the National Natural Science Foundation of China 相似文献
8.
Daniel W. Cunningham 《Archive for Mathematical Logic》2002,41(1):49-54
Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥Θ
L
(ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.
Received: 29 October 1999 / Published online: 12 December 2001 相似文献
9.
Yong Ding Senhua Lan 《分析论及其应用》2006,22(4):339-352
Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 < p < 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 < p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn). 相似文献
10.
A. Nemirovskii 《Mathematical Programming》1996,73(2):175-198
We establish polynomial time convergence of the method of analytic centers for the fractional programming problemt→min |x∈G, tB(x)−A(x)∈K, whereG ⊂ ℝ
n
is a closed and bounded convex domain,K ⊂ ℝ
m
is a closed convex cone andA(x):G → ℝ
n
,B(x):G→K are regular enough (say, affine) mappings.
This research was partly supported by grant #93-012-499 of the Fundamental Studies Foundation of Russian Academy of Sciences 相似文献