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2 results on '"Optimization with dynamics embedded"'

1. Local optimization of dynamic programs with guaranteed satisfaction of path constraints.

Author

Fu, Jun, Faust, Johannes M.M., Chachuat, Benoît, and Mitsos, Alexander

Subjects
*MATHEMATICAL optimization, *CONSTRAINT satisfaction, *ITERATIVE methods (Mathematics), *APPROXIMATION theory, *OPTIMAL control theory
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. [ABSTRACT FROM AUTHOR]

Published
2015
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2. Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Author

Johannes M.M. Faust, Jun Fu, Alexander Mitsos, and Benoît Chachuat

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
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.

Published
2015

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