We consider Bayesian information collection, in which a measurement policy collects information to support a future decision. This framework includes problems in ranking and selection, reinforcement learning, and continuous global optimization. We give sufficient conditions under which measurement policies achieve asymptotically minimal expected loss. Achieving asymptotically minimal expected l...

We provide an overview and some recent results on real-time communication and control over Gaussian channels. In particular, the problem of remote stabilization of linear systems driven by Gaussian noise over Gaussian relay channels is considered. Necessary and sufficient conditions for mean-square stabilization are presented, which reveal signal-to-noise ratio requirements for stabilization wh...

In this paper we study a class of perturbed constrained nonconvex variational problems depending on either time/state or time/state’s derivative variables. Its (optimal) value function is proved to be convex and then several related properties are obtained. Existence, strong duality results, and necessary/sufficient optimality conditions are established. Moreover, via a necessary optimality con...

This study investigates the global optimality of approximate dynamic programming (ADP) based solutions using neural networks for optimal control problems with fixed final time. Issues including whether or not the cost function terms and the system dynamics need to be convex functions with respect to their respective inputs are discussed and sufficient conditions for global optimality of the res...

In this paper, we investigate a minimax complex programming problem. Several sufficient Optimality conditions are established under the framework of generalized convexity for analytic functions. Employing the sufficient optimality conditions, we have proved the weak, strong and strict converse duality theorems for the complex minimax programming problem.

In this paper, Fritz-John type optimality conditions for weak efficient solutions in terms of contingent epiderivatives of vector variational inequalities and vector optimization problems with constraints are derived. Under assumptions on quasiconvexity of scalar functions, Fritz-John type necessary optimality conditions become Fritz-John type sufficient optimality conditions. Mathematics Subje...

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...

New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions – holding without any constraint qualification – are proved for singleor multi-objective constrained optimization prob...