# Multiple-Gradient Descent Algorithm (MGDA)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : In a previous report [Split of Territories, INRIA Research Report 6108], a methodology for the numerical treatment of a two-objective optimization problem, possibly subject to equality constraints, was proposed. The method was devised to be adapted to cases where an initial design-point is known and such that one of the two disciplines, considered to be preponderant, or fragile, and said to be the *primary discipline*, achieves a local or global optimum at this point. Then, a particular split of the design variables was proposed to accomplish a *competitive-optimization* phase by a Nash game, whose equilibrium point realizes an improvement of a *secondary discipline*, while causing the least possible degradation of the primary discipline from the initial optimum. In this new report, the initial design point and the number of disciplines are arbitrary. Certain theoretical results are established and they lead us to define a preliminary *cooperative-optimization* phase throughout which all the criteria improve, by a so-called *Multiple-Gradient Descent Algorithm (MGDA)*, which generalizes to $n$ disciplines ($n \geq 2$) the classical steepest-descent method. This phase is conducted until a design-point on the Pareto set is reached; then, the optimization is interrupted or continued in a subsequent competitive phase by a generalization of the former approach by territory splitting and Nash game.
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Reports
[Research Report] RR-6953, INRIA. 2009, pp.17

https://hal.inria.fr/inria-00389811
Contributor : Jean-Antoine Désidéri <>
Submitted on : Monday, November 5, 2012 - 10:59:40 AM
Last modification on : Tuesday, March 22, 2016 - 1:27:48 AM

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• HAL Id : inria-00389811, version 3

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Jean-Antoine Désidéri. Multiple-Gradient Descent Algorithm (MGDA). [Research Report] RR-6953, INRIA. 2009, pp.17. <inria-00389811v3>

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