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mxObjective functions come in several flavors, listed below. Each is described further at the linked webpage.
Links
[1] https://openmx.ssri.psu.edu/wiki/mxAlgebraObjective-help
[2] https://openmx.ssri.psu.edu/wiki/mxFIMLObjective-help
[3] https://openmx.ssri.psu.edu/wiki/mxMLObjective-help
[4] https://openmx.ssri.psu.edu/wiki/mxRAMObjective-help
[5] https://openmx.ssri.psu.edu/wiki/mxRObjective-help
[6] https://openmx.ssri.psu.edu/wiki/mxRowObjective-help