### Abstract

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

Original language | English (US) |
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Pages (from-to) | 423-453 |

Number of pages | 31 |

Journal | Journal of Mathematical Biology |

Volume | 61 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics

### Cite this

*Journal of Mathematical Biology*,

*61*(3), 423-453. https://doi.org/10.1007/s00285-009-0306-3

}

*Journal of Mathematical Biology*, vol. 61, no. 3, pp. 423-453. https://doi.org/10.1007/s00285-009-0306-3

**An analytical approach to the problem of inverse optimization with additive objective functions : An application to human prehension.** / Terekhov, Alexander V.; Pesin, Yakov B.; Niu, Xun; Latash, Mark; Zatsiorsky, Vladimir M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An analytical approach to the problem of inverse optimization with additive objective functions

T2 - An application to human prehension

AU - Terekhov, Alexander V.

AU - Pesin, Yakov B.

AU - Niu, Xun

AU - Latash, Mark

AU - Zatsiorsky, Vladimir M.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

AB - We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

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UR - http://www.scopus.com/inward/citedby.url?scp=77954035300&partnerID=8YFLogxK

U2 - 10.1007/s00285-009-0306-3

DO - 10.1007/s00285-009-0306-3

M3 - Article

VL - 61

SP - 423

EP - 453

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 3

ER -