Optimization Technologies Center OPTEX (OPTEX Ltd.)


1.SOLVEX Fortran Libraries - numerical algorithms package which includes routines for unconctrained, nonlinear constrained, global minimization and multicriterial optimization (more than 20 various algorithms).

Optimization - Routines

Unconstrained Minimization

Ellipsoid UEL
R-algorithm of Shor URS
Powell-Brent UPB
Modified Newton UMN

Minimization with simple Bounds

Direct search UBDS
Random search UBRS
Coordinates descent UBCD
Steepest descent UBSD
Conjugate gradient UBCG

Nonlinear Constrained Minimization

Ellipsoid NEL
Possible directions NPD
Linearized function NLF
Parametrized function NPAF
Penalty function NPEF
Dual Lagrange NDUL
Direct Lagrange NDIL
Modified Newton NMN

Constrained Global Minimization

Nonuniform covering GNC
Cluster search GCS
Genetic GGEN

Multicriterion Optimization

Additive convolution MAC
Chebyshev convolution MCC
Goal programming MGP
Epsilon approximation MEA

Service Routines

Admissible point ADMP
Forward-difference gradient FDGRAD


SOLVEX for WINDOWS and SOLVEX OCX - optimization system for OCX (VBX) and WINDOWS applications.

SOLVEX is integrated application software intended for the following:

solution of nonlinear constrained optimization problems;
solution of multi-variables global optimization problems;
solution of nonlinear multicriterial problems;
symbolic transformation and preprocessing of problem description;
creation the effective of algorithm combinations relying on hierarchical
structure of algorithms library (more than 150 various variants);
demonstration graphics;


Purposes: Solution of nonlinear optimization problems - constrained and unconstrained function minimization, search of global extremum of multi-variables nonlinear function, multicriterial Pareto-search and Pareto-approximation;

symbolic computation;

Applications: You can use SOLVEX for solving your problem directly, for including into application program, or as add-on tool for well-recognised mathematical systems (Mathematica, Matlab, MathCad etc.);
powerful algorithms library, module structure, special interface and VBX standard enables both a professional and nonprofessional users to solve difficult mathematical problems quickly and effectively.

Mode of operation: Symbolic expressions or DLL code for problems description;ODBC interface, open architecture for connection to external programs (VBX format).

Main system units

Optimization Algorithms library

Unconstrained minimization: Direct search method, conjugate gradients algorithm, conjugate directions Powell's and transform space gradients algorithms;

Constrained minimization: Penalty functions method, parametrization algorithm, modified Lagrange functions method;

Global (multi-extremal) optimization: non-uniform covering algorithms, cluster algorithm, genetic algorithms;

Multi-criterial (Pareto search) optimization: Convolution (including goal programming) and direct approximation algorithms.

Symbolic computation module

Calculus: Differentiation and integration, interval algebra;
Equation solving: Analytic solution of system of equations or unequalitys,Open Base of rules and trace of resolution.

Graphics module

Plots: superposition of elementary functions, parametrization functions, serial graphics, region of attractions, graphics for demonstration of the optimization process dynamic.

Microsoft Windows Version SOLVEX 3.1

System requirements: 80486 or higher, Windows 3.1 or later, 1 Mb HDD
User interface: Windows user interface and graphics
(MS-DOS Version SOLVEX 2.0 is available )