These constraints put a limit on our achieving optimality
as we undertake a heuristic decision-making process that simultaneously attempts at resolving all constraints resulting in sub-optimal but good enough (satisficing) decisions.
Before introducing our concept of event-specific optimality
, it will help if we briefly consider how others have attempted to incorporate choice into theories and models of causation.
As mentioned above, we concentrate on exponential preferences for both the agent and the principal, which allow us to get explicit solutions for optimality
N-MUSA model is a Nonlinear Goal Programing (NLGP) with a convex objective function, which ensures the global optimality
of the derived optimal solution.
From Theorem 21, we obtain the following sufficient optimality
condition for ([SP.sub.1]).
The basic framework of an optimal control is to prove the existence of the optimal control and then characterize the optimal control through optimality
In a general approach to ensure delay optimality
for multihop cooperative networks, one needs a problem formulation via Markov Decision Process (MDP), for example, [25, 26].
The well-known KKT optimality
conditions for problem (23) are stated as below.
In this communication, first several new classes of generalized second-order (ph, , o, p, p, th, m)-invex functions are introduced, and then these are applied to establish a set of second-order necessary optimality
conditions leading to several sets of second-order sufficient optimality
conditions and theorems for the following discrete minmax fractional programming problem:
In section 5, we present the necessary conditions of optimality
. For illustration of the abstract results, section 6 is devoted to some examples of linear quadratic regulator problems of meanfield type.
Penot,  and Cambini et al.,  established second-order necessary optimality
conditions for a point to be a local minimum and a local maximimum, respectively, for problem (P) using the theory of second-order projective tangent cones for twice Frechet differentiable objective functions as well as a sufficient optimality
condition of the same type.