0024608: Development of methods of global optimization of multivariable function

math_GlobOptMin - new global optimization minimization algorithm
Extrema_GlobOptFuncCC, Extrema_ExtCC, Extrema_ExtCC2d - implementation of GlobOptMin algorithm to extrema curve / curve
Extrema_CurveCache - deleted as obsolete code
ChFi3d_Builder.cxx  - fixed processing of extrema
math_NewtonMinimum.cxx - fixed step to avoid incorrect behavior
Test cases modification to meet new behavior.

src/math/math_GlobOptMin.hxx

@@ -0,0 +1,101 @@
+// Created on: 2014-01-20
+// Created by: Alexaner Malyshev
+// Copyright (c) 2014-2014 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#ifndef _math_GlobOptMin_HeaderFile
+#define _math_GlobOptMin_HeaderFile
+
+#include <math_MultipleVarFunction.hxx>
+#include <NCollection_Sequence.hxx>
+#include <Standard_Type.hxx>
+
+//! This class represents Evtushenko's algorithm of global optimization based on nonuniform mesh.<br>
+//! Article: Yu. Evtushenko. Numerical methods for finding global extreme (case of a non-uniform mesh). <br>
+//! U.S.S.R. Comput. Maths. Math. Phys., Vol. 11, N 6, pp. 38-54.
+
+class math_GlobOptMin
+{
+public:
+
+  Standard_EXPORT math_GlobOptMin(math_MultipleVarFunction* theFunc,
+                                 const math_Vector& theA,
+                                 const math_Vector& theB,
+                                 Standard_Real theC = 9);
+
+  Standard_EXPORT void SetGlobalParams(math_MultipleVarFunction* theFunc,
+                                       const math_Vector& theA,
+                                       const math_Vector& theB,
+                                       Standard_Real theC = 9);
+
+  Standard_EXPORT void SetLocalParams(const math_Vector& theLocalA,
+                                      const math_Vector& theLocalB);
+
+  Standard_EXPORT ~math_GlobOptMin();
+
+  Standard_EXPORT void Perform();
+
+  //! Get best functional value.
+  Standard_EXPORT Standard_Real GetF();
+
+  //! Return count of global extremas. NbExtrema <= MAX_SOLUTIONS.
+  Standard_EXPORT Standard_Integer NbExtrema();
+
+  //! Return solution i, 1 <= i <= NbExtrema.
+  Standard_EXPORT void Points(const Standard_Integer theIndex, math_Vector& theSol);
+
+private:
+
+  math_GlobOptMin & operator = (const math_GlobOptMin & theOther);
+
+  Standard_Boolean computeLocalExtremum(const math_Vector& thePnt, Standard_Real& theVal, math_Vector& theOutPnt);
+
+  void computeGlobalExtremum(Standard_Integer theIndex);
+
+  //! Check that myA <= pnt <= myB
+  Standard_Boolean isInside(const math_Vector& thePnt);
+
+  Standard_Boolean isStored(const math_Vector &thePnt);
+  
+  Standard_Boolean isDone();
+
+  // Input.
+  math_MultipleVarFunction* myFunc;
+  Standard_Integer myN;
+  math_Vector myA; // Left border on current C2 interval.
+  math_Vector myB; // Right border on current C2 interval.
+  math_Vector myGlobA; // Global left border.
+  math_Vector myGlobB; // Global right border.
+
+  // Output.
+  Standard_Boolean myDone;
+  NCollection_Sequence<Standard_Real> myY;// Current solutions.
+  Standard_Integer mySolCount; // Count of solutions.
+
+  // Algorithm data.
+  Standard_Real myZ;
+  Standard_Real myC; //Lipschitz constant
+  Standard_Real myE1; // Border coeff.
+  Standard_Real myE2; // Minimum step size.
+  Standard_Real myE3; // Local extrema starting parameter.
+
+  math_Vector myX; // Current modified solution
+  math_Vector myTmp; // Current modified solution
+  math_Vector myV; // Steps array.
+
+  Standard_Real myF; // Current value of Global optimum.
+};
+
+const Handle(Standard_Type)& TYPE(math_GlobOptMin);
+
+#endif