co(A): the convex hull of a set A, supp(Q): the support of a measure Q ∈ M, suppP(g(X θ)): the support of g(X θ) when X is distributed according to P ∈ M, s(Q θ): the dimension of the co(suppP(g(X θ))). The principal challenge in deriving our optimality result is establishing part (a) of Theorem 3.1. For ease of exposition, we provide an outline of the proof of this claim before its formal deri...

and Applied Analysis 3 subject to the nonlinear system (8), for Q ∈ R, R ∈ Rm×m positive semidefinite and positive definite matrices, respectively. Since the performance index (9) is convex, the following extreme necessary conditions are also sufficient for optimality [28]: ?̇? = f (t, x) + g (t, x) u ∗ , ̇ λ = −H x (x, u ∗ , λ) , u ∗ = arg min u H(x, u, λ) , x (t 0 ) = x 0 , λ (t f ) = 0, (10) w...

We consider scheduling in networks with interference constraints and reconfiguration delays, which may be incurred when one service schedule is dropped and a distinct service schedule is adopted. Reconfiguration delays occur in a variety of communication settings, such as satellite, optical or delay tolerant networks. In the absence of reconfiguration delays it is well known that the celebrated...

co(A): the convex hull of a set A, supp(Q): the support of a measure Q ∈ M, suppP(g(X θ)): the support of g(X θ) when X is distributed according to P ∈ M, s(Q θ): the dimension of the co(suppP(g(X θ))). The principal challenge in deriving our optimality result is establishing part (a) of Theorem 3.1. For ease of exposition, we provide an outline of the proof of this claim before its formal deri...

The individual and interactive effects of initial pH, temperature and initial substrate concentration on the growth of Clostridium pasteurianum was investigated in this study. Statistics based experimental designs are applied to optimize the process parameters for biomass concentration. The biomass concentration (g/l) was evaluated at various levels of initial substrate concentration, temperatu...

Amethodology is developed to add runs to existing supersaturated designs. The technique uses information from the analysis of the initial experiment to choose the best possible follow-up runs. After analysis of the initial data, factors are classified into one of three groups: primary, secondary, and potential. Runs are added to maximize a Bayesian D-optimality criterion to increase the informa...

A second order sufficient optimality criterion is presented for a multiobjective problem subject to a constraint given just as a set. To this aim, we first refine known necessary conditions in such a way that the sufficient ones differ by the replacement of inequalities by strict inequalities. Furthermore, we show that no relationship holds between this criterion and a sufficient multipliers ru...

Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,l986]. This paper studies the problem of finding an optimal approximating tree. The star­ decomposition scheme for sets of three binary variables [Lazarsfeld,l966; Pearl,1986] is shown to enhance the class of probability distributions that can support tree structures; such structures are called tree...

Nonlinear constrained optimal control problems as a rule suffer from the so-called two-norm discrepancy, which in particular says that under stable optimality conditions the objective functionals satisfy a quadratic local growth estimate in terms of the L2 norms but in L∞ neighborhoods of the solution only. Furthermore, in the case of weak local optima with continuous control functions, stabili...

In plug-and-play (PnP) regularization, the knowledge of forward model is combined with a powerful denoiser to obtain state-of-the-art image reconstructions. This typically done by taking proximal algorithm such as FISTA or ADMM, and formally replacing map associated regularizer nonlocal means, BM3D CNN denoiser. Each iterate resulting PnP involves some kind inversion followed denoiser-induced r...