Browsing Computational and Applied Mathematics by Title
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On the Constants in Inverse Inequalities in L2
(201005)In this paper we determine the constants in multivariate Markov inequalities in the L2norm on an interval, a triangle and a tetrahedron. Using orthonormal polynomials, we derive explicit expression for the constants on ... 
On the Construction of Strong Complementarity Slackness for DEA Linear Programming Problems Using a PrimalDual InteriorPoint Method
(199411)A novel approach for solving the DEA linear programming problems using a primaldual interiorpoint method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and ... 
On the Convergence of an Active Set Method for L1 Minimization
(201007)We analyze an abridged version of the activeset algorithm FPC_AS for solving the L1regularized least squares problem. The active set algorithm alternatively iterates between two stages. In the first "nonmonotone line ... 
On the Convergence of InteriorPoint Methods to the Center of the Solution Set in Linear Programming
(199109)The notion of the central path plays an important role in the convergence analysis of interiorpoint methods. Many interiorpoint algorithms have been developed based on the principle of following the central path, either ... 
On the Convergence of the Iteration Sequence in PrimalDual InteriorPoint Methods
(199108)This research is concerned with the convergence of the iteration sequence generated by a primaldual interiorpoint method for linear programming. It is known that this sequence converges when both the primal and the dual ... 
On the Convergence of the MizunoToddYe Algorithm to the Analytic Center of the Solution Set
(199212)In this work we demonstrate that the MizunoToddYe predictor corrector primaldual interiorpoint method for linear programming generates iteration sequences that converge to the analytic center of the solution set. 
On the Convergence of the Tapia Indicators in the Absence of Strict Complementarity
(199309)The convergence and the convergence rate of the Tapia indicators were established in ElBakry and ElBakry, Tapia and Zhang in the context of primaldual interiorpoint method under the assumption of strict complementarity. ... 
On the Convergence Rate of Newton InteriorPoint Methods in the Absence of Strict Complementarity
(199505)In the absence of strict complementarity, Monteiro and Wright proved that the convergence rate for a class of Newton interiorpoint methods for linear complementarity problems is at best linear. They also established an ... 
On the Coupling of Finite Volume and Discontinuous Galerkin Method for Elliptic Problems
(201003)The coupling of cellcentered finite volume method with primal discontinuous Galerkin method is introduced in this paper for elliptic problems. Convergence of the method with respect to the mesh size is proved. Numerical ... 
On the Decay Rate of Hankel Singular Values and Related Issues
(200105)This paper investigates the decay rate of the Hankel singular values of linear dynamical systems. This issue is of considerable interest in model reduction by means of balanced truncation, for instance, since the sum of ... 
On the Equivalence Between a Commonly Used Correlation Coefficient and a Least Squares Function
(200301)Many objective functions have been proposed in Xray crystallography to solve the molecular replacement (MR) problem and other optimization problems. In this paper, we establish the equivalence between optimizing two target ... 
On the Formulation of the PrimalDual Newton InteriorPoint Method for Nonlinear Programming
(199212)In this work we first study in detail the formulation of the primaldual interiorpoint method for linear programming. We show that, contrary to popular belief, it cannot be viewed as the damped Newton's method applied to ... 
On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers
(201207)The formulation min f(x)+g(y) subject to Ax+By=b arises in many application areas such as signal processing, imaging and image processing, statistics, and machine learning either naturally or after variable splitting. In ... 
On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior Point Newton Method for Nonlinear Programming
(199509)In this work we consider a linesearch globalization of the local primaldual interiorpoint Newton method for nonlinear programming recently introduced by ElBakry, Tapia, Tsuchiya and Zhang. Our linesearch uses a merit ... 
On the Matrix Cuts of Lovász and Schrijver and Their Use in Integer Programming
(200103)An important approach to solving many discrete optimization problems is to associate the discrete set (over which we wish to optimize) with the 01 vectors in a given polyhedron and to derive linear inequalities valid for ... 
On the Optimal Design of Columns Against Buckling
(199006)We establish existence, derive necessary conditions, and construct and test an algorithm for the maximization of a column's Euler buckling load under a variety of boundary conditions over a general class of admissible ... 
On the Parametrization of Illposed Inverse Problems Arising from Elliptic Partial Differential Equations
(200609)Electric impedance tomography (EIT) consists in finding the conductivity inside a body from electrical measurements taken at its surface. This is a severely illposed problem: any numerical inversion scheme requires some ... 
On the Quadratic Convergence of the Simplified MizunoToddYe Algorithm for Linear Programming
(199212)It is known that the MizunoToddYe predictorcorrector primaldual Newton interiorpoint method generates a duality gap sequence which converges quadratically to zero, and this is accomplished with an iteration complexity ... 
On the Quadratic Convergence of the Singular Newton's Method
(199212)The purpose of this essay is to describe a situation that we have found particularly exciting in our recent work in interiorpoint methods for linear programming. To our surprise, we have seen considerable theory developed ...