Jan 15, 2015The importance of VI: that they provide a theory in which to test existance/uniqueness of solutions, and algorithms to find those solutions!!Scholarly articles for convex optimization game theory
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Jan 15, 2015The importance of VI: that they provide a theory in which to test existance/uniqueness of solutions, and algorithms to find those solutions!!
Lexicographic optimization is a kind of Multi-objective optimization.
In general, multi-objective optimization deals with optimization problems with two or more objective functions to be optimized simultaneously.
Often, the different objectives can be ranked in order of importance to the decision-maker, so that objective mwe-math-element> is the most important, objective mwe-math-element> is the next most important, and so on.
Lexicographic optimization presumes that the decision-maker prefers even a very small increase in mwe-math-element>, to even a very large increase in mwe-math-element> etc.
Similarly, the decision-maker prefers even a very small increase in mwe-math-element>, to even a very large increase in mwe-math-element> etc.
In other words, the decision-maker has lexicographic preferences, ranking the possible solutions according to a lexicographic order of their objective function values.
Lexicographic optimization is sometimes called preemptive optimization, since a small increase in one objective value preempts a much larger increase in less important objective values.
