Generally, vagueness is modelled by a fuzzy approach and randomness by a stochastic approach. But in some cases, a decision maker may prefer using interval numbers as coefficients of an inexact relationship. In this paper, we define a linear programming problem involving interval numbers as an extension of the classical linear programming problem to an inexact environment. By using a new simple...

For unconstrained optimization, an inexact Newton algorithm is proposed recently, in which the preconditioned conjugate gradient method is applied to solve the Newton equations. In this paper, we improve this algorithm by efficiently using automatic differentiation and establish a new inexact Newton algorithm. Based on the efficiency coefficient defined by Brent, a theoretical efficiency ratio ...

Edge-based data structures are used to improve computational efficiency of Inexact Newton methods for solving finite element nonlinear solid mechanics problems on unstructured meshes. Edge-based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix-vector products needed in the inner iterative driver of the Inexact Newton method. Numerical experime...

In this paper we introduce a local convergence theory for Least Change Secant Update methods. This theory includes most known methods of this class, as well as some new interesting quasi-Newton methods. Further, we prove that this class of LCSU updates may be used to generate iterative linear methods to solve the Newton linear equation in the Inexact-Newton context. Convergence at a ¡j-superlin...

The finite element discretization of the incompressible steady-state Navier-Stokes equations yields a non-linear problem, due to the convective terms in the momentum equations. Several methods may be used to solve this non-linear problem. In this work we study Inexact Newton-type methods, associated with the SUPG/PSPG stabilized finite element formulation. The resulting systems of equations are...

MSC: 65K10 90C25 90C30 Keywords: Mixed variational inequalities Implicit methods Resolvent operator Inexact methods Self-adaptive rules a b s t r a c t In this paper, we suggest and analyze an inexact implicit method with a variable parameter for mixed variational inequalities by using a new inexactness restriction. Under certain conditions, the global convergence of the proposed method is prov...

We study inexact proximal Newton-type methods to solve convex optimization problems in composite form: minimize x∈Rn f(x) := g(x) + h(x), where g is convex and continuously differentiable and h : R → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. Proximal Newton-type methods require the solution of subproblems to obtain the search ...

Given a pair of graphs with the same number vertices, inexact graph matching problem consists in finding correspondence between vertices these that minimizes total number...

In this paper we examine parameterized procedural abstraction. This is an extension of an optimization whose sole purpose is to reduce code size. Previously published implementations of procedural abstraction have produced space savings if the instruction sequences are exact matches. We show that permanent space savings (compaction) are possible when (1) covering all inexact matches by several ...

Contrary to the existing techniques to realize inexact circuits that relied mostly on scaling of supply voltage or pruning of “leastsignificant” components in conventional correct circuits to achieve cost (energy, delay and/or area) and accuracy tradeoffs, we propose a novel technique called Probabilistic Logic Minimization which relies on synthesizing an inexact circuit in the first place resu...