Now showing items 1-10 of 37
A Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming
The choice of the centering (or barrier) parameter and the step length parameter are the fundamental issues in primal-dual interior-point algorithms for linear programming. Various choices for these two parameters have ...
Trace Regularity for a Second Order Hyperbolic Equation with Nonsmooth Coefficients
In this research, a trace regularity theorem on a time like surface is proved for the solution of a multidimensional linear acoustic wave equation with nonsmooth coefficients. Our theorem indicates that with microlocal ...
A Pseudopolynomial Network Flow Formulation for Exact Knapsack Separation
The NP-complete separation problem for the knapsack polyhedron P is formulated as a side-constrained network flow problem with a pseudopolynomial number of vertices and edges. It is demonstrated that the primal polyhedron ...
Gravitational Forces in Dual-Porosity Models of Single Phase Flow
A dual porosity model is derived by the normal theory of homogenization. The model properly incorporates gravity in that it respects the equilibrium states of the medium.
Extending the Farkas Lemma Approach to Necessity Conditions to Infinite Programming
Under mild assumptions, the classical Farkas lemma approach to Lagrange multiplier theory is extended to an infinite programming formulation. The main result generalizes the usual first-order necessity conditions to address ...
A Study of Indicators for Identifying Zero Variables in Interior-Point Methods
The ability to identify zero variables early on in an iterative method is of considerable value and can be used to computational advantage. In this work we first give a formal presentation of the notion of indicators for ...
Convergence Properties of the Barzilai and Borwein Gradient Method
In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. ...
Sizing the BFGS and DFP Updates: A Numerical Study
In this study we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained ...