This tutorial is the first comprehensive introduction to (possibly infinite) linear systems containing strict inequalities and evenly convex sets. The book introduces their application to convex optimization. Particular attention is paid to evenly convex polyhedra and finite linear systems containing strict inequalities. The book also analyzes evenly convex and quasiconvex functions from a conjugacy and duality perspective. It discusses the applications of these functions in economics. Written in an expository style the main concepts and basic results are illustrated with suitable examples and figures.

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María D. Fajardo studied Mathematics at the University of Murcia, Spain and received her Ph.D. in Mathematics from the University of Alicante under the supervision of Marco A. López, with a thesis on convex semi-infinite programming. She is an Associate Professor in the Department of Mathematics at the University of Alicante. Her main research fields are duality theory and evenly convex optimization, currently working on saddle point theory, Lagrangian duality and DC problems under even convexity assumptions.

Miguel A. Goberna is B.Sc and Ph.D. in Mathematics from the University of Valencia, Spain. He has held faculty positions at the Universities of Valencia and Alicante, where he is currently full Professor. He has been Head of several Departments at the University of Alicante and has served as Editor-in-Chief of the Springer journal Top. Miguel A. Goberna is author of more than 100 papers on semi-infinite and infinite optimization, robust optimization, duality, stability, even convexity, etc. He is best known for his books on linear semi-infinite optimization with Marco A. López (Wiley 1998 and Springer 2014).

Margarita M.L. Rodríguez is an Associate Professor in the Department of Mathematics at the University of Alicante, Spain. She earned her B.Sc. in Mathematics from the University of Santiago de Compostela and obtained her Ph.D. in Mathematics from the University of Alicante under the supervision of Miguel A. Goberna and Valentín Jornet with a thesis on linear systems and convex sets. Her research interests are focused on semi-infinite optimization, duality and even convexity, among others.

José Vicente-Pérez received both his M.Sc. and Ph.D. in Mathematics from the University of Murcia, Spain. He has held faculty positions at Public University of Navarre, University of New South Wales and Carlos III University of Madrid. After four years in the Department of Economic Analysis of the University of Alicante, he is currently Assistant Professor at the Department of Mathematics. He has published in international journals such as European Journal of Operational Research, SIAM Journal on Optimization, Journal of Optimization Theory and Applications and Journal of Public Economic Theory. His research interests include evenly convex sets and functions, polynomial optimization, decision making under uncertainty, etc.

Inhalt

Evenly convex sets - Linear systems containing strict inequalities.- Evenly convex polyhedra - Finite linear systems containing strict inequalities.- Evenly quasiconvex functions.- Evenly convex functions.- Extensions to infinite-dimensional spaces.