An efficient trust region method for unconstrained discrete-time optimal control problems

Coleman, Thomas F.; Liao, Aiping

doi:10.1007/bf01299158

Cited by 19 publications

(12 citation statements)

References 15 publications

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“…Unconstrained problems that we deal with are benchmark test problems from [3,21,24] and randomly generated test problems with artificial correlative sparsity. Constrained test problems (section 6.2) are chosen from [8] and optimal control problems [2].…”

Section: Numerical Resultsmentioning

confidence: 99%

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Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

Waki¹,

Kim²,

Kojima³

et al. 2006

SIAM J. Optim.

402

547

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Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of the supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite program (SDP) relaxations are obtained. Numerical results from various test problems are included to show the improved performance of the SOS and SDP relaxations.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Each F k is regarded as the index set of variables x i of the polynomial f k . For example, if n = 4 and f k (x) = x 3 1 + 3x 1 x 4 − 2x 2 4 , then F k = {1, 4}. Define the n × n (symbolic, symmetric) csp matrix R such that…”

Section: Correlative Sparsity In Inequality Constrained Popsmentioning

confidence: 99%

Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

Waki¹,

Kim²,

Kojima³

et al. 2006

SIAM J. Optim.

402

547

View full text Add to dashboard Cite

show abstract

“…However, we note that the Mystic software mentioned previously does in practice implement a formulation that relies on trust regions. Coleman and Liao incorporated a trust region to the stagewise Newton procedure, an algorithm similar but not identical to DDP [66].…”

Section: Global Convergencementioning

confidence: 99%

A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

Lantoine

Russell

2012

J Optim Theory Appl

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A new algorithm is presented to solve constrained nonlinear optimal control problems, with an emphasis on highly nonlinear dynamical systems. The algorithm, called HDDP, is a hybrid variant of differential dynamic programming, a proven second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. The new hybrid method incorporates nonlinear mathematical programming techniques to increase efficiency: quadratic programming subproblems are solved via trust region and range-space active set methods, an augmented Lagrangian cost function is utilized, and a multiphase structure is implemented. In addition, the algorithm decouples the optimization from the dynamics using first-and second-order state transition matrices. A comprehensive theoretical description of the algorithm is provided in this first part of the two paper series. Practical implementation and numerical evaluation of the algorithm is presented in Part 2.

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“…Similar methods have been further developed by Liao and Shoemaker (Liao and Shoemaker, 1991). Another method, the trust region method, was proposed by Coleman and Liao (Coleman and Liao, 1995) for the solution of unconstrained discrete-time optimal control problems. Although confined to the unconstrained problem, this method works for large scale minimization problems.…”

Section: Define a Hamiltonian Function Asmentioning

confidence: 99%

Informatics in Control, Automation and Robotics II

2007

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An efficient trust region method for unconstrained discrete-time optimal control problems

Cited by 19 publications

References 15 publications

Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

Informatics in Control, Automation and Robotics II

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