Hadamard type inequality for quasiconvex functions in higher dimensions
- Authors: Rubinov, Alex , Dutta, J.
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 270, no. 1 (2002), p. 80-91
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- Description: In this article we study a Hadamard type inequality for nonnegative evenly quasiconvex functions. The approach of our study is based on the notion of abstract convexity. We also provide an explicit calculation to evaluate the asymptotically sharp constant associated with the inequality over a unit square in the two-dimensional plane. © 2002 Elsevier Science (USA). All rights reserved.
- Description: 2003000149
Hermite-Hadamard-type inequalities for increasing convex-along-rays function
- Authors: Rubinov, Alex , Dragomir, S. S , Dutta, J.
- Date: 2004
- Type: Text , Journal article
- Relation: Analysis Vol. 24, no. 2 (2004), p. 171-181
- Full Text: false
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- Description: C1
- Description: 2003000933
Hidden abstract convex functions
- Authors: Rubinov, Alex , Wu, Zhiyou , Li, Duan
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Nonlinear and Convex Analysis Vol. 6, no. 1 (2005), p. 203-216
- Full Text: false
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- Description: C1
- Description: 2003001424
Comparative analysis of numerical solution of optimal control problems
- Authors: Shangareeva, Gulnaz , Grigoryev, Igor , Mustafina, Svetlana
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal of Pure and Applied Mathematics Vol. 110, no. 4 (2016), p. 645-649
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- Description: In this article step by step algorithms were developed for solving optimal control problems based on the method of successive approximations and the method of variations in the space of controls. The algorithm of the method of successive approximations requires details of the problem to the boundary problem of the maximum principle. In turn, the algorithm of the variations is more versatile because it is based on iterating state variables and control in the phase space. A numerical study and comparative analysis of the developed algorithms performed at different values of accuracy. © 2016 Academic Publications, Ltd.
About subdifferential calculus for abstract convex functions
- Authors: Sharikov, Evgenii
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Nonlinear and Convex Analysis Vol. 8, no. 2 (2007), p. 257-275
- Full Text: false
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- Description: We introduce a stronger version of the strong globalization property of Rolewicz and examine the corresponding subdifferential calculus for abstract convex functions. In particular, we calculate a formula for the abstract subdifferential of the maximum of a finite set of abstract convex functions. We also present some examples of families of functions, which possess this new strong globalization property.
- Description: C1
- Description: 2003005856
Super antimagic total labeling of graphs
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2008
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 76, no. (2008), p. 161-171
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- Description: Let G = (V, E) be a simple, finite and undirected graph with v vertices and e edges, A graph labeling is a mapping from elements of a graph to a set of numbers (usually positive integers). If the domain of the mapping is the set of vertices (or edges) then the labeling is called vertex-labeling (or edge-labeling). If the domain of the mapping is the set of vertices and edges then the labeling is called total labeling. The sum of all labels associated with a graph element is called the weight of the element. If the weights of vertices (or the weights of edges) form an arithmetic progression starting at a and with difference d, then the labeling is called (a, d)-vertex-antimagic (or (a, d)-edge-antimagic). Such a labeling is called v-super (or e-super) if the smallest labels appear on the vertices (or edges). In this paper we present new results for v-super vertex-antimagic total and e-super edge-antimagic total labeling.
- Description: C1
Face antimagic labelings of prisms
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2006
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 71, no. (Nov 2006), p. 269-286
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- Description: This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every number s, the s-sided face weights form an arithmetic progression of difference d. In this paper, we investigate d-antimagic labelings for prism for d is an element of {7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 26,27,30,36).
- Description: C1
Super edge-antimagic total labeling
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2006
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 71, no. (2006), p. 131-141
- Full Text: false
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- Description: A (p, q)-graph G is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1,2,...,p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Moreover, G is said to be super (a, d)-edge-antimagic total if f(V(G)) = {1,2,..., p}. In this paper we study the super (a,d)-edge-antimagic total properties of certain classes of graphs, including ladders, generalized prisms and antiprisrns.
- Description: C1
- Description: 2003001596
On several classes of monographs
- Authors: Sugeng, Kiki Ariyanti , Ryan, Joe
- Date: 2007
- Type: Text , Journal article
- Relation: Australasian Journal of Combinatorics Vol. 37, no. (2007), p. 277-284
- Full Text: false
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- Description: C1
- Description: 2003004943
New constructions of A-magic graphs using labeling matrices
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 147-151
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A generalization of the Remez algorithm to a class of linear spline approximation problems with constraints on spline parameters
- Authors: Sukhorukova, Nadezda
- Date: 2008
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 23, no. 5 (2008), p. 793-810
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- Description: The classical Remez algorithm was developed for constructing the best polynomial approximations for continuous and discrete functions in an interval [a, b]. In this paper, the classical Remez algorithm is generalized to the problem of linear spline approximation with certain conditions on the spline parameters. Namely, the spline parameters have to be nonnegative and the values of the splines at one of the borders (or both borders) of the approximation intervals may be fixed. This type of constraint occurs in some practical applications, e.g. the problem of taxation tables restoration. The results of the numerical experiments with a Remez-like algorithm developed for this class of conditional optimization problems, are presented.
- Description: C1
Aggregate subgradient smoothing mehtods for large scale nonsmooth nonconvex optimisation and applications
- Authors: Sultanova, Nargiz
- Date: 2015
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 91, no. 3 (2015), p. 523-524
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- Description: Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, for example in engineering, machine learning and economics. In addition, some smooth problems can be reformulated as nonsmooth optimisation problems with a simpler structure or a smaller dimension. Despite the fact that there exist many algorithms for solving nonsmooth optimisation problems, the field is still very much in development. Nonsmooth nonconvex optimisation, in particular, is far from being considered a mature branch of optimisation.
Calculating the extremal number ex (v ; {C3, C4, ..., Cn})
- Authors: Tang, Jianmin , Lin, Yuqing , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 27, no. (2006), p. 101-102
- Full Text: false
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- Description: This paper introduces and analyzes a parallel method of simulated annealing. Borrowing from genetic algorithms, an effective combination of simulated annealing and genetic algorithms, called parallel recombinative simulated annealing, is developed. This new algorithm strives to retain the desirable asymptotic convergence properties of simulated annealing, while adding the populations approach and recombinative power of genetic algorithms. The algorithm iterates a population of solutions rather than a single solution, employing a binary recombination operator as well as a unary neighborhood operator. Proofs of global convergence are given for two variations of the algorithm. Convergence behavior is examined, and empirical distributions are compared to Boltzmann distributions. Parallel recombinative simulated annealing is amenable to straightforward implementation on SIMD, MIMD, or shared-memory machines. The algorithm, implemented on the CM-5, is run repeatedly on two deceptive problems to demonstrate the added implicit parallelism and faster convergence which can result from larger population sizes.
- Description: C1
HSAGA and its application for the construction of near-Moore digraphs
- Authors: Tang, Jianmin , Miller, Mirka , Lin, Yuqing
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Discrete Algorithms Vol. 6, no. 1 (2008), p. 73-84
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- Description: The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. This paper deals with directed graphs. General upper bounds, called Moore bounds, exist for the largest possible order of such digraphs of maximum degree d and given diameter k. It is known that simulated annealing and genetic algorithm are effective techniques to identify global optimal solutions. This paper describes our attempt to build a Hybrid Simulated Annealing and Genetic Algorithm (HSAGA) that can be used to construct large digraphs. We present our new results obtained by HSAGA, as well as several related open problems. © 2007 Elsevier B.V. All rights reserved.
- Description: C1
Divisibility conditions in almost Moore digraphs with selfrepeats
- Authors: Teska, Jakub , Kuzel, Roman , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 24, no. (2006), p. 161-163
- Full Text: false
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- Description: Moore digraph is a digraph with maximum out-degree d, diameter k and order Md, k = 1 + d + ... + dk. Moore digraphs exist only in trivial cases if d = 1 (i.e., directed cycle Ck) or k = 1 (i.e., complete symmetric digraph). Almost Moore digraphs are digraphs of order one less than Moore bound. We shall present new properties of almost Moore digraphs with selfrepeats from which we prove nonexistence of almost Moore digraphs for some k and d. © 2006 Elsevier B.V. All rights reserved.
- Description: C1
Some new characterizations of intrinsic transversality in hilbert spaces
- Authors: Thao, Nguyen , Bui, Hoa , Cuong, Nguyen , Verhaegen, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 5-39
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- Description: Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties. © 2020, The Author(s).
Directional metric pseudo subregularity of set-valued mappings: a general model
- Authors: Van Ngai, Huynh , Tron, Nguyen , Van Vu, Nguyen , Théra, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 61-87
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- Description: This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established. © 2019, Springer Nature B.V.
Dynamics of positive multiconvex relations
- Authors: Vladimirov, Alexander , Rubinov, Alex
- Date: 2001
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 8, no. 2 (2001), p. 387-399
- Full Text: false
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- Description: A notion of multiconvex relation as a union of a finite number of convex relations is introduced. For a particular case of multiconvex process, that is, a union of a finite set of convex processes, we define the notions of the joint and the generalized spectral radius in the same manner as for matrices. We prove the equivalence of these two values if all component processes are positive, bounded, and closed. © Heldermann Verlag.
Quasilinear Mappings, M-Ideals and Popyhedra
- Authors: Yost, David
- Date: 2012
- Type: Text , Conference paper
- Relation: Operators and Matrices Vol. 6, p. 279-286
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- Description: We survey the connection between two results from rather different areas: failure of the 3-space property for local convexity (and other properties) within the category of quasi-Banach spaces, and the irreducibility (in the sense of Minkowski difference) of large families of finite dimensional polytopes.
- Description: C1
Strictly convex banach algebras
- Authors: Yost, David
- Date: 2021
- Type: Text , Journal article
- Relation: Axioms Vol. 10, no. 3 (2021), p.
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- Description: We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C