Mathematics – Optimization and Control
Scientific paper
2009-05-08
Mathematics
Optimization and Control
35 pages
Scientific paper
The worthwhile-to-move incremental principle is a mechanism where, at each step, the agent, before moving and after exploration around the current state, compares intermediate advantages and costs to change to advantages and costs to stay. These advantages and costs to change include goal-setting, psychological, cognitive, learning and inertia aspects. Acceptables moves are such that advantages to move than to stay are higher than some fraction of costs to move than to stay, with, as a result, a limitation of the intermediate sacrifices to reach the goal. When the agent is more goal-oriented and improves enough at each step, the process ends in a permanent routine, a rest point where the agent prefers to stay than to change, in spite of some possible residual frustration to have missed his goal. In case of high local costs to move this approach leads to a cognitive proof of Ekeland epsilon-variational principle. The as if hypothesis (as if agents would optimize) is revisited, leading to the introduction of a new class of optimization algorithm with inertia, the local search and proximal algorithms.
Attouch Hedy
Soubeyran Antoine
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