A penalized nonparametric method for nonlinear constrained optimization based on noisy data

Dias, Ronaldo; Garcia, Nancy L.; Zambom, Adriano Zanin

doi:10.1007/s10589-008-9185-6

Cited by 5 publications

(8 citation statements)

References 19 publications

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“…In this work our attention was focused on the extension of the proposed algorithm by [11] to incorporate the more realistic assumption of dependence among the sequential observations of the same obstacle. Dependence among the observations is a natural assumption.…”

Section: Resultsmentioning

confidence: 99%

“…, μ L }. Dias et al [11] proposes an approximate solution to the problem mentioned above. First, approximate the {0, ∞}-penalization by the smooth functional…”

Section: The Deterministic Problemmentioning

confidence: 99%

“…If the obstacles are perfectly seen, [11] proposes a non-parametric algorithm to approximate the best route. In Sect.…”

Section: Introductionmentioning

confidence: 99%

“…If there are only independent measurement errors, that is, the vectors (W ,k , V ,k ) are independent and identically distributed, [11] proposes a stochastic solution that converges to the deterministic one (Sect. 3.1).…”

Section: Introductionmentioning

confidence: 99%

“…In this work we follow the same ideas developed in [11] to obtain the best stochastic solution to the problem. The general idea is to consider only solutions belonging to a finite-dimensional approximating space generated by B-splines and to impose a penalization on solutions that do not comply with the constraints.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo algorithm for trajectory optimization based on Markovian readings

2010

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This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mechanism that corrects the sensors at each reading using the previous observation. The proposed algorithm is based on the penalized nonparametric method previously introduced that uses confidence ellipses as a fattening of the avoidance set. In this paper we obtain consistent estimates of the best trajectory using Monte Carlo construction of the confidence ellipse.

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Section: Resultsmentioning

confidence: 99%

“…, μ L }. Dias et al [11] proposes an approximate solution to the problem mentioned above. First, approximate the {0, ∞}-penalization by the smooth functional…”

Section: The Deterministic Problemmentioning

confidence: 99%

“…If the obstacles are perfectly seen, [11] proposes a non-parametric algorithm to approximate the best route. In Sect.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monte Carlo algorithm for trajectory optimization based on Markovian readings

2010

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Constrained optimization with stochastic feasibility regions applied to vehicle path planning

2015

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In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the sensors have measurement errors, the stochasticity of the data has to be incorporated into the models. In this paper, we consider using a genetic algorithm for the constrained optimization problem of finding the trajectory with minimum length between two locations, avoiding the obstacles on the way. To incorporate the variability of the sensor readings, we propose a modified genetic algorithm, addressing the stochasticity of the feasible regions. In this way, the probability that a possible solution in the search space, say x, is feasible can be derived from the random observations of obstacles and pathways, creating a real-time data learning algorithm. By building a confidence region from the observed data such that its border intersects with the solution point x, the level of the confidence region defines the probability that x is feasible. We propose using a smooth penalty function based on the Gaussian distribution, facilitating the borders of the feasible regions to be reached by the algorithm.

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Global optimization with spline constraints: a new branch-and-bound method based on B-splines

Grimstad

Sandnes

2015

J Glob Optim

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A penalized nonparametric method for nonlinear constrained optimization based on noisy data

Abstract: Autonomous vehicle, B-splines, Consistent estimator, Confidence ellipses, Constrained optimization, Nonparametric method,

Cited by 5 publications

References 19 publications

Monte Carlo algorithm for trajectory optimization based on Markovian readings

Monte Carlo algorithm for trajectory optimization based on Markovian readings

Constrained optimization with stochastic feasibility regions applied to vehicle path planning

Global optimization with spline constraints: a new branch-and-bound method based on B-splines

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