The Existence of Value and Saddle Point in Games of Fixed Duration

1985 ◽  
Vol 23 (2) ◽  
pp. 172-196 ◽  
Author(s):  
Leonard D. Berkovitz
Keyword(s):  
Saddle Point ◽  
Fixed Duration ◽  
Existence Of Value

scholarly journals Syntheses of differential games and pseudo-Riccati equations

2002 ◽  
Vol 7 (2) ◽  
pp. 61-83 ◽  
Author(s):  
Yuncheng You
Keyword(s):  
Dynamical Systems ◽  
Saddle Point ◽  
Riccati Equation ◽  
Differential Games ◽  
Regular Solution ◽  
Closed Loop ◽  
Optimal Strategies ◽  
Time Parameter ◽  
Fixed Duration ◽  
Linear Dynamical Systems

For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solutionP(t,x). Then the closed-loop optimal strategies are given byu(t)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(t,x(t)). For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.

CONSTITUTIONALISM AND AMENDMENTS TO THE BASIC LAW OF THE RUSSIAN FEDERATION 2020: POLITICAL ANALYSIS

2020 ◽  
Vol 15 (6) ◽  
pp. 103-118
Author(s):  
O.A. SIDENKO ◽  
◽  
D.V. SOSUNOV ◽  
Keyword(s):  
Russian Language ◽  
Constitutional Amendments ◽  
Expert Opinions ◽  
Political Analysis ◽  
Basic Law ◽  
Expert Assessments ◽  
The Russian Federation ◽  
Existence Of Value ◽  
Transitional Constitutionalism ◽  
The Impact

The purpose of the article is to reveal the contradictions of the Russian transitional constitutionalism of the 2020 model as perceived by experts. It is achieved by presenting a palette of experts' views on the phenomenon of constitutionalism, expert assessments of the impact of the 2020 constitutional reform on constitutional principles, the distance between citizens and authorities, as well as expert opinions on the existence of value consolidation between the state and civil society in modern Russia. It is extremely important that the constitutional amendments, contributing to adaptation to changing realities, remain within the framework of the system of constitutionalism. There is no relevant developed methodology for political and legal assessment in the Russian-language scientific literature. The research group, having resorted to an expert survey, proposed their own version. The results obtained indicate not only the importance of value connotations in the perception of constitutionalism by experts, the weakening of all groups of constitutional principles (negative assessments prevail over positive ones), the manipulative nature of the process, but also a potential increase in the distance between the governors and the governed. Nevertheless, the threshold values that could indicate the interpretation of constitutional novels by experts as leading to going beyond the framework of constitutionalism are not identified. Since the project is pilot and generalizations are based on expert estimates, the conclusions are debatable.

Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2557-2574 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Equality Constraints ◽  
New Class ◽  
Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

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