Fixed-Time Algorithms for Time-Varying Convex Optimization

To resolve the time-varying convex optimization problems with the cost function, the constraints or both being time dependent, in this brief we investigate a novel type of fixed-time algorithms. First, with the unconstrained time-varying optimization problem considered, a general framework algorithm...

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Published inIEEE transactions on circuits and systems. II, Express briefs Vol. 70; no. 2; pp. 616 - 620
Main Authors Hong, Huifen, Yu, Wenwu, Jiang, Guo-Ping, Wang, He
Format Journal Article
LanguageEnglish
Published New York IEEE 01.02.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Asymptotic stability
Computational geometry
Convergence
Convex functions
Convexity
Cost function
Design optimization
equality constraint
Fixed-time stability
Gradient flow
nonlinear system
Prediction algorithms
Stability criteria
Time dependence
time-varying optimization
Trajectory optimization
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Abstract To resolve the time-varying convex optimization problems with the cost function, the constraints or both being time dependent, in this brief we investigate a novel type of fixed-time algorithms. First, with the unconstrained time-varying optimization problem considered, a general framework algorithm is developed for tracking its optimal trajectory within fixed time, which contains the gradient flow-based scheme and Newton-type method as its special cases. Then, considering the equality constraint being involved in the time-varying optimization problem, we design another algorithm with fixed-time convergence, which includes Newton-type scheme as its special case. To verify that the given approach achieves fixed-time convergence, the simulation result is given with first-order Euler discretization.
AbstractList To resolve the time-varying convex optimization problems with the cost function, the constraints or both being time dependent, in this brief we investigate a novel type of fixed-time algorithms. First, with the unconstrained time-varying optimization problem considered, a general framework algorithm is developed for tracking its optimal trajectory within fixed time, which contains the gradient flow-based scheme and Newton-type method as its special cases. Then, considering the equality constraint being involved in the time-varying optimization problem, we design another algorithm with fixed-time convergence, which includes Newton-type scheme as its special case. To verify that the given approach achieves fixed-time convergence, the simulation result is given with first-order Euler discretization.
Author Wang, He
Jiang, Guo-Ping
Yu, Wenwu
Hong, Huifen
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SubjectTerms Algorithms
Asymptotic stability
Computational geometry
Convergence
Convex functions
Convexity
Cost function
Design optimization
equality constraint
Fixed-time stability
Gradient flow
nonlinear system
Prediction algorithms
Stability criteria
Time dependence
time-varying optimization
Trajectory optimization
Title Fixed-Time Algorithms for Time-Varying Convex Optimization
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Volume 70
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