A Class of Interaction Optimization Problems

In this paper, we introduce a class of interaction optimization problems in whichoptimality is generated through balance interaction among coupled components. Theproposed interaction optimization structure is formulated asminu∈X L1(u)subject toL2(u) ≥ α, L3(u) ≥ β,where the optimization structure is governed through interaction balance among coupledcomponents. Under differentiable Zulfia invexity and coupled mapping structures, weestablish the Balance KKT conditions as interaction optimality principle for interaction-generated optimization structures. We further show that classical optimization togetherwith the Kuhn-Tucker conditions are recovered as limiting cases when the interactionbalance components become inactive.