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There has been much recent progress in global optimization algo- rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun- damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon- vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was...

There has been much recent progress in global optimization algo- rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun- damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon- vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was...

A famous saying (due toHerriot)definescultureas "what remainswhen everythingisforgotten ." One couldparaphrase thisdefinitionin statingthat generalizedconvexity iswhat remainswhen convexity has been dropped . Of course, oneexpectsthatsome convexityfeaturesremain.For functions, convexity ofepigraphs(what is above thegraph) is a simplebut strong assumption.It leads tobeautifulpropertiesand to a field initselfcalled convex analysis. In several models, convexity is not presentandintroducing genuine convexityassumptionswouldnotberealistic. A simple extensionof thenotionof convexity consists in...