This paper proposes two sets of rules Rule G and Rule P for controlling step lengths in a generic primal dual interior point method for solving the linear program ming problem in standard form and its dual Theoretically Rule G ensures the global convergence while Rule P which is a special case of Rule G ensures the O nL iteration polynomial time computational complexity Both rules depend only o...

In this paper, we introduce the concept of dual frame of g-p-frame, and give the sufficient condition for a g-p-frame to have dual frames. Using operator theory and methods of functional analysis, we get some new properties of g-p-frame. In addition, we also characterize g-p-frame and g-q-Riesz bases by using analysis operator of g-p-Bessel sequence. c ©2017 All rights reserved.

Introduction. We let G denote an infinite compact group, and G its dual. We use the notation of our book [3, Chapters 7 and 8]. Recall that -4(G) denotes the Fourier algebra of G (an algebra of continuous functions on G), and J2f°°(G) denotes its dual space under the pairing ( / , # ) , ( / G A (G), 0 Ç if°°(G)). Further, note if°°(G) is identified with the G*-algebra of bounded operators on L(...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

We introduce and study the problem MUTUAL PLANAR DUALITY, which asks for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. Our algorithmic main result is an NP-completeness proof for the general case and a linear-time algorithm for biconnected graphs. To shed light onto the combinatorial structure of the duals of a planar graph, we consider the commo...

We show that the Laplace approximation of a supremum by L-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual P∗ appear naturally when using this simple approximation technique for the value function g of P or its Legendre-Fenchel conjugate g∗. In addition, minimizing the LBF of the dual P∗ is just e...

Let G = SpecA be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗ = R × B∗ as R-algebras and the first projection A∗ → R is the unit of A. If M is a dual functor of G-modules and wG := (1, 0) ∈ R×B ∗ =...