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Important power system planning and operation problems have been formulated as mathematical optimization problems. Such problems as the economic dispatch, in many of its facets; var scheduling and allocation; pollution dispatch; maximum interchange; hydrothermal unit commitment and dispatch; generation, transmission, and distribution expansion planning; maintenance scheduling and substation switching, have been formulated and solved. Modern mathematical optimization techniques, such as nonlinear, quadratic, linear, integer and dynamic programming and their many combinations and extensions, have been exploited. Some of the formulations and solutions to these problems as presented in the recent literature within the power systems field are reviewed. The large number of papers available is a measure of the current immense activity in this area. Attempts are made to point out some specific areas where more work needs to be done.