Tools for modelling support and construction of optimization applications

We argue the case for an open systems approach towards modelling and application support. We discuss how the 'usability' and 'skills' analysis naturally leads to a viable strategy for integrating application construction with modelling tools and optimizers. The role of the implementation environment is also seen to be critical in that it is retained as a building block within the resulting system

Reformulations of mathematical programming problems as linear complementarity problems

A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are (i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and unrestricted variables, (ii.) Minimum Linear Complementarity Problem (MLCP) which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized, (iii.) Second Minimum Linear Complementarity Problem (SMLCP) which is an MLCP but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. A number of well known mathematical programming problems, namely quadratic programming (convex, nonconvex, pseudoconvex nonconvex), bilinear programming, game theory, zero-one integer programming, the fixed charge problem, absolute value programming, variable separable programming are reformulated as members of this family of four complementarity problems

An enumerative method for the solution of linear complementarity problems

In this report an enumerative method for the solution of the Linear Complementarity Problem (LCP) is presented. This algorithm completely processes the LCP, and does not require any particular property of the LCP to apply. That is the algorithm terminates after either finding all the solutions of an LCP or establishing that no solution exists. The method is extended to also process the Second Linear Complementarity Problem (SLCP), a problem which has been introduced to represent the general quadratic program involving unrestricted variables

Modelling of mathematical programs: An analysis of strategy and an outline description of a computer assisted system

The salient components of the mathematical programming modeling activity are first analysed. Earlier generation systems such as program generators and procedural (modelling) languages are briefly discussed. A proposal for a computer assisted modelling scheme is then put forward. The proposed system contrasts with the earlier approaches in that no computer programming expertise is required on the part of the modeller. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. The philosophy and design of the experimental system supports this approach to model description. This aspect is illustrated by a few examples. The introduction of computer assistance in structuring of the data and the resulting model is novel and is in line with recent developments in friendly and flexible user interface

Alternative methods for representing the inverse of linear programming basis matrices

Methods for representing the inverse of Linear Programming (LP) basis matrices are closely related to techniques for solving a system of sparse unsymmetric linear equations by direct methods. It is now well accepted that for these problems the static process of reordering the matrix in the lower block triangular (LBT) form constitutes the initial step. We introduce a combined static and dynamic factorisation of a basis matrix and derive its inverse which we call the partial elimination form of the inverse (PEFI). This factorization takes advantage of the LBT structure and produces a sparser representation of the inverse than the elimination form of the inverse (EFI). In this we make use of the original columns (of the constraint matrix) which are in the basis. To represent the factored inverse it is, however, necessary to introduce special data structures which are used in the forward and the backward transformations (the two major algorithmic steps) of the simplex method. These correspond to solving a system of equations and solving a system of equations with the transposed matrix respectively. In this paper we compare the nonzero build up of PEFI with that of EFI. We have also investigated alternative methods for updating the basis inverse in the PEFI representation. The results of our experimental investigation are presented in this pape

Design, implementation and testing of an integrated branch and bound algorithm for piecewise linear and discrete programming problems within an LP framework

A number of discrete variable representations are well accepted and find regular use within LP systems. These are Binary variables, General Integer variables, Variable Upper Bounds or Semi Continuous variables, Special Ordered Sets of type One and type Two. The FortLP system has been extended to include these representations. A Branch and Bound algorithm is designed in which the choice of sub-problems and branching variables are kept general. This provides considerable scope of experimentation with tree development heuristics and the tree search can then be guided by search parameters specified by user subroutines. The data structures for representing the variables and the definition of the branch and bound tree are described. The results of experimental investigation for a few test problems are reported

Computer assisted mathematical programming

A Computer Assisted Mathematical Programming (Modelling) System (CAMPS) is described in this paper. The system uses program generator techniques for model creation and contrasts with earlier approaches which use a special purpose language to construct models. Thus no programming skill is required to formulate a model. In designing the system we have first analysed the salient components of the mathematical programming activity. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. Computer assistance is provided to structure the data and the resulting model in the above sequence. In addition to this novel feature and the automatic documentation facility, the system is in line with recent developments, and incorporates a friendly and flexible user interface

Deformation Projected RMF Calculation for Cr and Fe nuclei in Hybrid Derivative Coupling Model

The ground state properties of even mass Cr and Fe isotopes are studied using the generalized hybrid derivative coupling model. The energy surface of each isotope is plotted as a function of the mass quadrupole moment. The neutron numbers N=20 and N=40 are seen to remain magic numbers but N= 28 and 50 are predicted to be non-magic. The neutron number N=70 turns out to be a magic number according to the present calculation. In all the isotopes studied the calculated binding energy values are less than those obtained from experiment while the deformation is in better agreement.Comment: To appear in Int. Jour. Mod. Phys.