diff --git a/modules/core/include/opencv2/core/optim.hpp b/modules/core/include/opencv2/core/optim.hpp
index 4f1749ec97..18e733f47b 100644
--- a/modules/core/include/opencv2/core/optim.hpp
+++ b/modules/core/include/opencv2/core/optim.hpp
@@ -63,9 +63,11 @@ public:
     class CV_EXPORTS Function
     {
     public:
-       virtual ~Function() {}
-       virtual double calc(const double* x) const = 0;
-       virtual void getGradient(const double* /*x*/,double* /*grad*/) {}
+        virtual ~Function() {}
+        virtual int getDims() const = 0;
+        virtual double getGradientEps() const;
+        virtual double calc(const double* x) const = 0;
+        virtual void getGradient(const double* x,double* grad);
     };
 
     /** @brief Getter for the optimized function.
diff --git a/modules/core/src/conjugate_gradient.cpp b/modules/core/src/conjugate_gradient.cpp
index 90353cc7fd..1259cc9756 100644
--- a/modules/core/src/conjugate_gradient.cpp
+++ b/modules/core/src/conjugate_gradient.cpp
@@ -46,6 +46,25 @@
 
 namespace cv
 {
+    double MinProblemSolver::Function::getGradientEps() const { return 1e-3; }
+    void MinProblemSolver::Function::getGradient(const double* x, double* grad)
+    {
+        double eps = getGradientEps();
+        int i, n = getDims();
+        AutoBuffer<double> x_buf(n);
+        double* x_ = x_buf;
+        for( i = 0; i < n; i++ )
+            x_[i] = x[i];
+        for( i = 0; i < n; i++ )
+        {
+            x_[i] = x[i] + eps;
+            double y1 = calc(x_);
+            x_[i] = x[i] - eps;
+            double y0 = calc(x_);
+            grad[i] = (y1 - y0)/(2*eps);
+            x_[i] = x[i];
+        }
+    }
 
 #define SEC_METHOD_ITERATIONS 4
 #define INITIAL_SEC_METHOD_SIGMA 0.1
diff --git a/modules/core/src/downhill_simplex.cpp b/modules/core/src/downhill_simplex.cpp
index 158dca6dbf..a0cc1320b8 100644
--- a/modules/core/src/downhill_simplex.cpp
+++ b/modules/core/src/downhill_simplex.cpp
@@ -235,6 +235,7 @@ protected:
     inline void createInitialSimplex( const Mat& x0, Mat& simplex, Mat& step )
     {
         int i, j, ndim = step.cols;
+        CV_Assert( _Function->getDims() == ndim );
         Mat x = x0;
         if( x0.empty() )
             x = Mat::zeros(1, ndim, CV_64F);
diff --git a/modules/core/test/test_conjugate_gradient.cpp b/modules/core/test/test_conjugate_gradient.cpp
index d6b0908f85..a1fd6113c3 100644
--- a/modules/core/test/test_conjugate_gradient.cpp
+++ b/modules/core/test/test_conjugate_gradient.cpp
@@ -60,16 +60,19 @@ static void mytest(cv::Ptr<cv::ConjGradSolver> solver,cv::Ptr<cv::MinProblemSolv
 
 class SphereF_CG:public cv::MinProblemSolver::Function{
 public:
+    int getDims() const { return 4; }
     double calc(const double* x)const{
         return x[0]*x[0]+x[1]*x[1]+x[2]*x[2]+x[3]*x[3];
     }
-    void getGradient(const double* x,double* grad){
+    // use automatically computed gradient
+    /*void getGradient(const double* x,double* grad){
         for(int i=0;i<4;i++){
             grad[i]=2*x[i];
         }
-    }
+    }*/
 };
 class RosenbrockF_CG:public cv::MinProblemSolver::Function{
+    int getDims() const { return 2; }
     double calc(const double* x)const{
         return 100*(x[1]-x[0]*x[0])*(x[1]-x[0]*x[0])+(1-x[0])*(1-x[0]);
     }
diff --git a/modules/core/test/test_downhill_simplex.cpp b/modules/core/test/test_downhill_simplex.cpp
index 9370f3172d..47c73f9751 100644
--- a/modules/core/test/test_downhill_simplex.cpp
+++ b/modules/core/test/test_downhill_simplex.cpp
@@ -68,11 +68,13 @@ static void mytest(cv::Ptr<cv::DownhillSolver> solver,cv::Ptr<cv::MinProblemSolv
 
 class SphereF:public cv::MinProblemSolver::Function{
 public:
+    int getDims() const { return 2; }
     double calc(const double* x)const{
         return x[0]*x[0]+x[1]*x[1];
     }
 };
 class RosenbrockF:public cv::MinProblemSolver::Function{
+    int getDims() const { return 2; }
     double calc(const double* x)const{
         return 100*(x[1]-x[0]*x[0])*(x[1]-x[0]*x[0])+(1-x[0])*(1-x[0]);
     }