preemptively scheduling a set of independent jobs with release time on one processor is a historical problem. in this paper, the same problem has been considered in which objective is to minimize the mean flow time. to prepare a perfect branch-and-bound, some optimality conditions have been represented and they have been compared with the optimality conditions which have been proposed before. o...

A common classifier for unlabeled nodes on undirected graphs uses label propagation from the labeled nodes, equivalent to the harmonic predictor on Gaussian random fields (GRFs). For active learning on GRFs, the commonly used V-optimality criterion queries nodes that reduce the L (regression) loss. V-optimality satisfies a submodularity property showing that greedy reduction produces a (1− 1/e)...

This letter proposes online algorithms for dynamic matching markets in power distribution systems. These address the problem of flexible loads with renewable generation, objective maximizing social welfare exchange system. More specifically, two are proposed generation-load scenarios: (i) when mean generation is greater than load, and (ii) condition reversed. With intuition that performance suc...

We propose a general geometry representation of d-level quantum system (or qudit for short). Then we define a general class of operations for qudits. A sufficient and necessary condition of when an operation in the class would be a legal quantum operation is found. This condition is expressed in terms of the quantum Fourier transform. As an application of this condition, we recover the optimal ...

We present a general necessary condition for separation of the reachable set of a Lipschitz control system from another given set of states, expressed in terms of an “approximating multicone” to the set in a sense that contains as special cases the Clarke and Mordukhovich cones. We then show how this separation result implies a strengthened form of the usual sufficient condition for local contr...

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case and for the uniform distribution, the least-squares method is optimal in expectation in [1] and in probability in [7]...

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the case of dependent data. For one parameter...

A common classifier for unlabeled nodes on undirected graphs uses label propagation from the labeled nodes, equivalent to the harmonic predictor on Gaussian random fields (GRFs). For active learning on GRFs, the commonly used V-optimality criterion queries nodes that reduce the L (regression) loss. V-optimality satisfies a submodularity property showing that greedy reduction produces a (1− 1/e)...

A weak maximal principle for minimax optimal control problems with mixed state-control equality and inequality constraints is provided. In the formulation of problem we allow parameter uncertainties in all functions involved: cost function, dynamical system constraints. Then a new constraint qualification Mangassarian-Fromovitz type introduced which allowed us to prove necessary conditions opti...

In this paper we derive for a controlled stochastic evolution system on Hilbert space H a sufficient condition for optimality. The result is derived by using its adjoint backward stochastic evolution equation.