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Local optimization of dynamic programs with guaranteed satisfaction of path constraints
- Publication Year :
- 2015
- Publisher :
- Elsevier Ltd, 2015.
-
Abstract
- An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequality-path-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in Mitsos (2011) to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: (i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; (ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; (iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies.
- Subjects :
- Mathematical optimization
Technology
Karush–Kuhn–Tucker conditions
Equations
Parameterization
Mathematical Sciences
Automation & Control Systems
Engineering
Uniform boundedness
Semi-infinite programs
Semiinfinite programs
Point (geometry)
Electrical and Electronic Engineering
Inequality constraint
Global optimization
Finite set
Path constraints
Mathematics
Sensitivity-analysis
Science & Technology
Systems
Engineering, Electrical & Electronic
Solver
Optimal control
Dynamic optimization
Industrial Engineering & Automation
Control and Systems Engineering
Path (graph theory)
Adaotuve convexification algorithm
Information And Computing Sciences
Alpha-method
State
Optimization with dynamics embedded
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....e042cd4637c8bf4f5a8bd823eae45265