共查询到20条相似文献,搜索用时 15 毫秒
1.
Balder’s well-known existence theorem (1983) for infinite-horizon optimal control problems is extended to the case in which the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part max{f0, 0} of the utility function (integrand) f0 is relaxed to the requirement that the integrals of f0 over intervals [T, T′] be uniformly bounded above by a function ω(T, T′) such that ω(T, T′) → 0 as T, T′→∞. This requirement was proposed by A.V. Dmitruk and N.V. Kuz’kina (2005); however, the proof in the present paper does not follow their scheme, but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given. 相似文献
2.
Ioannis K. Argyros 《Journal of Applied Mathematics and Computing》2009,31(1-2):97-111
We provide new sufficient convergence conditions for the semilocal convergence of Ulm’s method (Izv. Akad. Nauk Est. SSR 16:403–411, 1967) in order to approximate a locally unique solution of an equation in a Banach space setting. We show that in some cases, our hypotheses hold true but the corresponding ones (Burmeister in Z. Angew. Math. Mech. 52:101–110, 1972; Kornstaedt in Aequ. Math. 13:21–45, 1975; Petzeltova in Comment. Math. Univ. Carol. 21:719–725, 1980; Potra and Ptǎk in Cas. Pest. Mat. 108:333–341, 1983; Ulm in Izv. Akad. Nauk Est. SSR 16:403–411, 1967) do not. We also show that under the same hypotheses and computational cost as (Burmeister in Z. Angew. Math. Mech. 52:101–110, 1972; Kornstaedt in Aequ. Math. 13:21–45, 1975; Petzeltova in Comment. Math. Univ. Carol. 21:719–725, 1980; Potra and Ptǎk in Cas. Pest. Mat. 108:333–341, 1983; Ulm in Izv. Akad. Nauk Est. SSR 16:403–411, 1967) finer error sequences can be obtained. Numerical examples are also provided further validating the results. 相似文献
3.
Roberto Andreani Ellen H. Fukuda Paulo J. S. Silva 《Journal of Optimization Theory and Applications》2013,156(2):417-449
We propose a Gauss–Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by André and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of the KKT conditions as a system of equations. Such reformulation allows the use of a semismooth Newton method, so that local superlinear convergence rate can be proved under an assumption weaker than the usual strong second-order sufficient condition and without requiring strict complementarity. Besides, we note that the exact penalty function can be used to globalize the method. We conclude with some numerical experiments using the collection of test problems CUTE. 相似文献
4.
We present a new approach to Berndtssons complex extension of Prékopas theorem. This approach is inspired by the recent local proof of Prékopas theorem obtained by Ball, Barthe and Naor. In the complex setting, this approach leads to a formula expressing in terms of (derivatives of) where e–(z)= As a consequence, we obtain new conditions ensuring that is subharmonic when is plurisubharmonic. 相似文献
5.
Proceedings - Mathematical Sciences - 相似文献
6.
László Székelyhidi 《Monatshefte für Mathematik》2014,175(4):639-643
Fréchet’s functional equation \(\Delta _{y_1,y_2,\dots ,y_{n+1}}f=0\) plays a key role in the theory of polynomial functions. A basic theorem of Djokovi? shows that under general conditions the functional equation \(\Delta _y^{n+1}f=0\) is equivalent to Fréchet’s equation. Here we give a short alternative proof for this result using spectral synthesis. 相似文献
7.
§1.IntroductionThedomainoptimizationproblemisakindofshapeoptimizationproblem.Specifical-ly,wewanttofindadomain(whichiscaledop... 相似文献
8.
9.
By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation dX t = a θ (X t )dt + dZ t with a Lévy process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved. 相似文献
10.
Let G be a group of automorphisms of a ranked poset \({{\mathcal Q}}\) and let N k denote the number of orbits on the elements of rank k in \({{\mathcal Q}}\). What can be said about the N k for standard posets, such as finite projective spaces or the Boolean lattice? We discuss the connection of this question to the representation theory of the group, and in particular to the inequalities of Livingstone-Wagner and Stanley. We show that these are special cases of more general inequalities which depend on the prime divisors of the group order. The new inequalities often yield stronger bounds depending on the order of the group. 相似文献
11.
Let P,Q, and R denote the Ramanujan Eisenstein series. We compute algebraic relations in terms of P(q i ) (i=1,2,3,4), Q(q i ) (i=1,2,3), and R(q i ) (i=1,2,3). For complex algebraic numbers q with 0<|q|<1 we prove the algebraic independence over ? of any three-element subset of {P(q),P(q 2),P(q 3),P(q 4)} and of any two-element subset of {Q(q),Q(q 2),Q(q 3)} and {R(q),R(q 2),R(q 3)}, respectively. For all the results we use some expressions of $P(q^{i_{1}}), Q(q^{i_{2}}) $ , and $R(q^{i_{3}}) $ in terms of theta constants. Computer-assisted computations of functional determinants and resultants are essential parts of our proofs. 相似文献
12.
Andriy Bondarenko 《Discrete and Computational Geometry》2014,51(3):509-515
In this paper, we answer Larman’s question on Borsuk’s conjecture for two-distance sets. We find a two-distance set consisting of 416 points on the unit sphere $S^{64}\subset\mathbb{R}^{65}$ which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk’s conjecture is known to be false. Other examples of two-distance sets with large Borsuk numbers are given. 相似文献
13.
K. R. Kazmi 《Journal of Optimization Theory and Applications》2001,109(3):667-674
The -generalized minima for vector optimization problems are defined and a sufficient condition for the existence of -generalized minima for vector optimization problems is established. 相似文献
14.
Using a criterion due to Bourgain [10] and the generalization of the self-dual induction defined in [19], for each primitive permutation we build a large family of k-interval exchanges satisfying Sarnak’s conjecture, and, for at least one permutation in each Rauzy class, smaller families for which we have weak mixing, which implies a prime number theorem, and simplicity in the sense of Veech. 相似文献
15.
In 1970 Rédei and Megyesi proved that a set of
p points in
AG(2,p), p prime, is a line, or it determines at
least
directions. In 81
Lovász and Schrijver characterized the case of equality. Here we
prove that the number of determined directions cannot be between
and
. The upper bound
obtained is one less than the smallest known example. 相似文献
16.
Kazuki Okamura 《Aequationes Mathematicae》2016,90(6):1071-1085
We consider regularity for solutions of a class of de Rham’s functional equations. Under some smoothness conditions of functions making up the equation, we improve some results in Hata (Japan J Appl Math 2:381–414, 1985). Our results are applicable to some cases when the functions making up the equation are non-linear functions on an interval, specifically, polynomials and linear fractional transformations. Our results imply the singularity of some well-known singular functions, in particular, Minkowski’s question-mark function, and, some small perturbed functions of the singular functions. 相似文献
17.
We state an integer linear programming formulation for the unique characterization of complete simple games, i.e. a special subclass of monotone Boolean functions. In order to apply the parametric Barvinok algorithm to obtain enumeration formulas for these discrete objects we provide a tailored decomposition of the integer programming formulation into a finite list of suitably chosen sub-cases. As for the original enumeration problem of Dedekind on Boolean functions we have to introduce some parameters to be able to derive exact formulas for small parameters. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and a new enumeration formula for complete simple games with two minimal winning vectors. 相似文献
18.
We reconsider the classical problem of representing a finite number of
forms of degree d in the polynomial ring
over n + 1 variables as scalar combinations
of powers of linear forms.
We define a geometric construct called a grove, which,
in a number of cases, allows us to determine the dimension of the space of
forms which can be so represented for a fixed number of summands.
We also present two new examples, where this dimension turns out to
be less than what a naïve parameter count would predict. 相似文献
19.
Bo Ju Jiang 《数学学报(英文版)》2016,32(1):25-39
The Conway potential function(CPF) for colored links is a convenient version of the multivariable Alexander–Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's "smoothing of crossings" is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra P_nB_n, where B_n is a braid group and P_n is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander–Conway polynomial of knots. 相似文献
20.
Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl's theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl's theorem for f(T). 相似文献