convexityhasbeenincreasinglyimportantinrecentyearsinthestudyofextremumproblemsinmanyareasofappliedmathematics.thepurposeofthisbookistoprovideanexpositionofthetheoryofconvexsetsandfunctionsinwhichapplicationstoextremumproblemsplaythecentralrole.
systemsofinequalities,theminimumormaximumofaconvexfunctionoveraconvexset,lagrangemultipliers,andminimaxtheoremsareamongthetopicstreated,aswellasbasicresultsaboutthestructureofconvexsetsandthecontinuityanddifferentiabilityofconvexfunctionsandsaddle-functions.dualityisemphasizedthroughout,particularlyintheformoffenchersconjugacycorrespondenceforconvexfunctions.