Interval quadratic programming for day-ahead dispatch of uncertain predicted demand

Automatica ◽  
2016 ◽  
Vol 64 ◽  
pp. 163-173 ◽  
Author(s):  
Takayuki Ishizaki ◽  
Masakazu Koike ◽  
Nacim Ramdani ◽  
Yuzuru Ueda ◽  
Taisuke Masuta ◽  
...  
Keyword(s):  
Quadratic Programming ◽  
Interval Quadratic Programming

Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs

2016 ◽  
Vol 18 (01) ◽  
pp. 1650002
Author(s):  
Ajay Kumar Bhurjee
Keyword(s):  
Quadratic Programming ◽  
Equilibrium Point ◽  
Programming Problem ◽  
Equilibrium Points ◽  
Optimal Strategies ◽  
Bimatrix Game ◽  
Existence Of Equilibrium ◽  
Numerical Example ◽  
Closed Intervals ◽  
Interval Quadratic Programming

This paper deals a bimatrix game with payoffs as closed intervals. Existence of equilibrium point of this game is discussed by using suitable interval quadratic programming problem. Further, a methodology is proposed for finding optimal strategies for each player of the game. The methodology is illustrated by numerical example.

scholarly journals Solving Interval Quadratic Programming Problems by Using the Numerical Method and Swarm Algorithms

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. A. Elsisy ◽  
D. A. Hammad ◽  
M. A. El-Shorbagy
Keyword(s):  
Quadratic Programming ◽  
Numerical Method ◽  
Programming Problem ◽  
Numerical Solutions ◽  
Quadratic Programming Problem ◽  
New Approach ◽  
Swarm Algorithms ◽  
Quadratic Programming Problems ◽  
Chaotic Particle Swarm Optimization ◽  
Interval Quadratic Programming

In this paper, we present a new approach which is based on using numerical solutions and swarm algorithms (SAs) to solve the interval quadratic programming problem (IQPP). We use numerical solutions for SA to improve its performance. Our approach replaced all intervals in IQPP by additional variables. This new form is called the modified quadratic programming problem (MQPP). The Karush–Kuhn–Tucker (KKT) conditions for MQPP are obtained and solved by the numerical method to get solutions. These solutions are functions in the additional variables. Also, they provide the boundaries of the basic variables which are used as a start point for SAs. Chaotic particle swarm optimization (CPSO) and chaotic firefly algorithm (CFA) are presented. In addition, we use the solution of dual MQPP to improve the behavior and as a stopping criterion for SAs. Finally, the comparison and relations between numerical solutions and SAs are shown in some well-known examples.

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