We transform the system of nonlinear equations into a nonlinear programming problem, which is solved by null space algorithms. We do not use standard least square approach. We divide the equations into two groups. One group contains the equations that are treated as equality constraints. The square of other equations is regarded as objective function. … Read more
In the paper it is shown how to utilize the flexibility in native Java arrays for matrix computations. Suitable datastructures for symmetric and sparse matrices are introduced. A disadvantage of the native Java arrays is shown when used as two-dimensional array for dense matrix computation. Numerical results show that the efficiency is not lost using … Read more
Filter approach is recently proposed by Fletcher and Leyffer in 2002 and is attached importance to. In this paper, the filter approach is used in an sequential penalty quadratic programming (S$l$QP) algorithm which is similar to that of Yuan’s. In every trial step, the step length is controlled by a trust region radius. If the … Read more
The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z_* := min_x {c’x | Ax-b \in C_Y, x \in C_X }, to the more general non-conic format: (GP_d): z_* := min_x {c’x | Ax-b \in C_Y, x \in P}, where P is … Read more
The Watson Sparse Matrix Package (WSMP) is a high-performance robust direct solver for both symmetric and unsymmetric large sparse systems of linear equations. Currently, it works in serial, multi-threaded parallel, message-passing parallel, and a combination of message-passing and multi-threaded modes on IBM RS6000 with AIX and IA32 with Linux. The symmetric solver has features to … Read more
The aim of this paper is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented making use of two general iscreteapproximation methods. Simultaneously, we discuss the consistenceand the epi-convergence of the asymptotic approximation problem. CitationSchool of … Read more
Column generation has become a powerful tool in solving large scale integer programs. We argue that most of the often reported compatibility issues between pricing oracle and branching rules disappear when branching decisions are based on the reduction of the variables of the oracle’s domain. This can be generalized to branching on variables of a … Read more
We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach … Read more
An operation on trivalent graphs leads from the truncated cube to buckminsterfullerene, and C60 is the only fullerene with disjoint pentagons which can be obtained by this method. The construction and the proof emphasize maximal independent sets that contain two fifths of the vertices of trivalent graphs. In the case of C60, these sets define … Read more
This paper presents an annotated bibliography on interior point methods for solving network flow problems. We consider single and multi-commodity network flow problems, as well as preconditioners used in implementations of conjugate gradient methods for solving the normal systems of equations that arise in interior network flow algorithms. Applications in electrical engineering and miscellaneous papers … Read more