Two-sided game for competitive systems with non-local interactions

S. Lenhart; V. Protopopescu; S. Stojanovic

doi:10.1109/cdc.1990.203755

Two-sided game for competitive systems with non-local interactions

S. Lenhart, V. Protopopescu, S. Stojanovic

Research output: Contribution to journal › Conference article › peer-review

Abstract

A system of two stationary semilinear elliptic partial differential equations (PDEs) with rather general competitive interactions is considered. The motivation is related to possible applications of the formalism to competitive/conflict situations and, in particular, to classical warfare for which systems of this type have been applied with rather promising results. The optimal strategies, mathematically defined in terms of minimizing or maximizing a certain function, are realized by varying the control functions. The purpose of this study is to show that a unique saddle point exists and is represented by the solution of the optimality system. The optimality system consists of two elliptic PDE state equations coupled with two adjoint equations.

Original language	English
Pages (from-to)	1030-1031
Number of pages	2
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2
DOIs	https://doi.org/10.1109/cdc.1990.203755
State	Published - 1990
Externally published	Yes
Event	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: Dec 5 1990 → Dec 7 1990

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10.1109/cdc.1990.203755

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abstract = "A system of two stationary semilinear elliptic partial differential equations (PDEs) with rather general competitive interactions is considered. The motivation is related to possible applications of the formalism to competitive/conflict situations and, in particular, to classical warfare for which systems of this type have been applied with rather promising results. The optimal strategies, mathematically defined in terms of minimizing or maximizing a certain function, are realized by varying the control functions. The purpose of this study is to show that a unique saddle point exists and is represented by the solution of the optimality system. The optimality system consists of two elliptic PDE state equations coupled with two adjoint equations.",

author = "S. Lenhart and V. Protopopescu and S. Stojanovic",

year = "1990",

doi = "10.1109/cdc.1990.203755",

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journal = "Proceedings of the IEEE Conference on Decision and Control",

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AU - Lenhart, S.

AU - Protopopescu, V.

AU - Stojanovic, S.

PY - 1990

Y1 - 1990

N2 - A system of two stationary semilinear elliptic partial differential equations (PDEs) with rather general competitive interactions is considered. The motivation is related to possible applications of the formalism to competitive/conflict situations and, in particular, to classical warfare for which systems of this type have been applied with rather promising results. The optimal strategies, mathematically defined in terms of minimizing or maximizing a certain function, are realized by varying the control functions. The purpose of this study is to show that a unique saddle point exists and is represented by the solution of the optimality system. The optimality system consists of two elliptic PDE state equations coupled with two adjoint equations.

AB - A system of two stationary semilinear elliptic partial differential equations (PDEs) with rather general competitive interactions is considered. The motivation is related to possible applications of the formalism to competitive/conflict situations and, in particular, to classical warfare for which systems of this type have been applied with rather promising results. The optimal strategies, mathematically defined in terms of minimizing or maximizing a certain function, are realized by varying the control functions. The purpose of this study is to show that a unique saddle point exists and is represented by the solution of the optimality system. The optimality system consists of two elliptic PDE state equations coupled with two adjoint equations.

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DO - 10.1109/cdc.1990.203755

M3 - Conference article

AN - SCOPUS:0025559792

SN - 0191-2216

VL - 2

SP - 1030

EP - 1031

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)

Y2 - 5 December 1990 through 7 December 1990

ER -

Two-sided game for competitive systems with non-local interactions

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