Construction of convex continuations for functions defined on a hypersphere

Stoyan, Yu. G.; Yakovlev, Sergiy; Emets, O. A.; Valuiskaya, O. A.

doi:10.1007/bf02742066

Cited by 20 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 4. [22] Each of the systems of equations (35), (40) defines a strict continuous functional representation of E nk (G).…”

Section: Example 5 (B ′mentioning

confidence: 99%

See 1 more Smart Citation

Continuous Extensions On Euclidean Combinatorial Configurations

Pichugina¹,

Yakovlev²

2022

BASM

View full text Add to dashboard Cite

In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.

show abstract

“…Theorem 4. [22] Each of the systems of equations (35), (40) defines a strict continuous functional representation of E nk (G).…”

Section: Example 5 (B ′mentioning

confidence: 99%

“…The proposed typology of Euclidean combinatorial configurations will be the basis for algorithms of their continuous representation and functional extensions. The beginning of such research was laid in the papers [19][20][21][22][24][25][26]40,43,46].…”

Section: Introductionmentioning

confidence: 99%

Continuous Extensions On Euclidean Combinatorial Configurations

Pichugina¹,

Yakovlev²

2022

BASM

View full text Add to dashboard Cite

show abstract

“…Methods are developed [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] for solving many classes of combinatorial optimization problems, and these methods can also be used for solving combinatorial game-type optimization problems; in particular, the combinatorial truncation method for combinatorial problems on permutations and arrangements [24][25][26][27][28][29][30] can be used for finding an optimal strategy for a player under combinatorial constraints.…”

mentioning

confidence: 99%

Games with combinatorial constraints

Yemets

Ustian

2008

Cybern Syst Anal

View full text Add to dashboard Cite

‡ UDC 519.85Decision-making criterions are applied to the determination of optimal player's strategies in combinatory game-type optimization problems in which combinatory constraints that are imposed on the strategies of one player are determined by permutations and nature acts as the second player.Decision-making under uncertainty is an important problem since many economic processes describe conflict situations in which participants achieve their objectives using various ways, and none of them know in advance how the others will act. Such situations are studied in game theory (see, for example, [1-7]) whose destination is the development of recommendations concerning a better behavior in a concrete situation.In [8][9][10][11][12], a new class of game problems is formulated and investigated, namely, combinatorial game-type optimization problems in which, for one or both players, combinatorial constraints are imposed on the use of their strategies. Methods are developed [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] for solving many classes of combinatorial optimization problems, and these methods can also be used for solving combinatorial game-type optimization problems; in particular, the combinatorial truncation method for combinatorial problems on permutations and arrangements [24][25][26][27][28][29][30] can be used for finding an optimal strategy for a player under combinatorial constraints.In investigating combinatorial game-type optimization, problems were considered in which combinatorial constraints determined by permutations were imposed on the strategy of one player, and the other player was nature [12]. Such problems can be considered as specific "games with nature" (see, for example, [6,7]). In the classical game theory, various criteria are considered in solving such problems rather than only the maximin criterion that was used for finding solutions of combinatorial game-type optimization problems in [12]. The use of one criterion or another in decision-making under conflict for each concrete situation will allow one to find the most adequate variant of actions of a player and, hence, it makes sense to consider the application of well-known criteria to combinatorial game-type optimization problems.In the present article, we investigate the use of various well-known decision-making criteria for combinatorial game-type optimization problems in which combinatorial constraints determined by permutations are imposed on the strategy of one player and the other player is nature. The determination of optimal player strategies for each criterion is investigated.In [12], an economic problem of farming industry is formulated. Problem. A farm grows m sorts of crops on its m fields. Field areas are different and, hence, the yield of each grown culture depends on the field on which it is planted. Moreover, the yield of each grown crop and, hence, the farm profit depends on weather. It is necessary to develop a plan of growing crops that is optimal in a sense.This problem was considered ...

show abstract

“…Recently, a great many works are published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] that are devoted to the investigation of problems of combinatorial optimization and problems of fractional-linear programming. But problems on Euclidean combinatorial sets with homographic objective functions are insufficiently investigated.…”

mentioning

confidence: 99%

“…For sets of permutations, arrangements, combinations, polypermutations, and others, a part of these problems is solved [4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

mentioning

confidence: 99%

A Nonreducible System of Constraints of a Combinatorial Polyhedron in a Linear-Fractional Optimization Problem on Arrangements

Yemets

Chernenko

2005

Cybern Syst Anal

View full text Add to dashboard Cite

A system of linear constraints is investigated. The system describes the domain of feasible solutions of a linear optimization problem to which a linear-fractional optimization problem on arrangements is reduced. A system of nonreducible constraints of a polyhedrom is established for the linear-fractional optimization problem on arrangements.Introduction. Recently, a great many works are published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] that are devoted to the investigation of problems of combinatorial optimization and problems of fractional-linear programming. But problems on Euclidean combinatorial sets with homographic objective functions are insufficiently investigated.During the investigation of problems of Euclidean combinatorial optimization, the need arises for the description of convex envelopes of definite combinatorial sets, disclosure and substantiation of properties of sets of feasible solutions of such problems, and development of methods of solution of these problems. For sets of permutations, arrangements, combinations, polypermutations, and others, a part of these problems is solved [4][5][6][7][8][9][10][11][12][13][14][15][16][17].In [11], a nonreducible system of linear constraints of a general polyhedron of permutations is established. In [15], a theorem on redundant constraints of the system of inequalities of a combinatorial polyhedron in a linear-fractional optimization problem on permutations is proved. In [16], a nonreducible system of constraints for a general polyhedron of arrangements is established. Based on the investigated properties of Euclidean combinatorial optimization problems, algorithms for solution of these problems are proposed (see, for example [10,17] ) .The existence of optimization problems with homographic objective functions on arrangements requires the development of efficient optimization methods and algorithms that make it possible to solve individual problems and classes of such problems. This necessitates the study of properties of such optimization problems.Statement of the problem. In this article, we investigate a system of linear constraints of a combinatorial polyhedron for a problem with a linear objective function to which the problem on arrangements with a homographic objective function is reduced.Presentation of the basic material of this investigation with a complete substantiation of the scientific results obtained. We introduce the necessary terminology and cite facts from [7]. A multiset G g g g = { }

show abstract

Construction of convex continuations for functions defined on a hypersphere

Cited by 20 publications

References 0 publications

Continuous Extensions On Euclidean Combinatorial Configurations

Continuous Extensions On Euclidean Combinatorial Configurations

Games with combinatorial constraints

A Nonreducible System of Constraints of a Combinatorial Polyhedron in a Linear-Fractional Optimization Problem on Arrangements

Contact Info

Product

Resources

About