Consistency retrieval from a biased relative preference table is an imperative task in decision theory This paper considers the least squares approximation of a pairwise comparison matrix by consistent matrices It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the component wise logarithmic transformation A rst order optimality con...

We obtain error estimates for the numerical approximation of a distributed control problem governed by the stationary Navier–Stokes equations, with pointwise control constraints. We show that the L2-norm of the error for the control is of order h2 if the control set is not discretized, while it is of order h if it is discretized by piecewise constant functions. These error estimates are obtaine...

We prove an extension of Yuan’s Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality conditions in the presence of equality and inequality constraints. SIAM J. Opt., 15(2):394–408, 2005], where the classical necessary second-order optimality co...

For the Helmholtz equation (with wavenumber k) and analytic curves or surfaces Γ we analyze the Galerkin discretization of classical combined field integral equations in an L-setting. We give abstract conditions on the approximation properties of the ansatz space that ensure stability and quasi-optimality of the Galerkin method. Special attention is paid to the hp-version of the boundary elemen...

The multiobjective bilevel program is a sequence of two optimization problems, with the upper-level problem being multiobjective and the constraint region of the upper level problem being determined implicitly by the solution set to the lower-level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of all lower-level problems near...

The generalized likelihood ratio test (GLRT), which is commonly used in composite hypothesis testing problems, is investigated. Conditions for asymptotic optimality of the GLRT in the NeymanPearson sense are studied and discussed. First, a general necessary and sufficient condition is established, and then based on this, a sufficient condition, which is easier to verify, is derived. A counterex...

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both rowand column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-ro...

We study a stationary, single-stage inventory system, under periodic review, with fixed ordering costs and multiple sales levers (such as pricing, advertising, etc.). We show the optimality of (s, S)-type policies in these settings under both the backordering and lost-sales assumptions. Our analysis is constructive, and is based on a condition which we identify as being key to proving the (s, S...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

It is well-known that the power-of-d choices routing algorithm maximizes throughput and heavy-traffic optimal in load balancing systems with homogeneous servers. However, if servers are heterogeneous, optimality does not hold general. We find necessary sufficient conditions for of when we prove almost same to show optimality. Additionally, generalize condition a larger class policies.