diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/SimplexOptimizerTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/SimplexOptimizerTest.java
index 25dd7c897..732ba42de 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/SimplexOptimizerTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/SimplexOptimizerTest.java
@@ -17,6 +17,10 @@
 package org.apache.commons.math4.legacy.optim.nonlinear.scalar.noderiv;
 
 import java.util.Arrays;
+import java.io.PrintWriter;
+import java.io.IOException;
+import java.nio.file.Files;
+import java.nio.file.Paths;
 import org.junit.jupiter.api.Assertions;
 import org.junit.jupiter.api.Test;
 import org.junit.jupiter.api.extension.ParameterContext;
@@ -222,6 +226,111 @@ public class SimplexOptimizerTest {
             Assertions.assertTrue(nEval < functionEvaluations,
                                   name + ": nEval=" + nEval);
         }
+
+        /**
+         * Asserts that the lowest function value (along a line starting at
+         * {@link #start} is reached at the {@link #optimum}.
+         *
+         * @param numPoints Number of points at which to evaluate the function.
+         * @param plot Whether to generate a file (for visual debugging).
+         */
+        public void checkAlongLine(int numPoints,
+                                   boolean plot) {
+            if (plot) {
+                final String name = createPlotBasename(function, start, optimum);
+                try (PrintWriter out = new PrintWriter(Files.newBufferedWriter(Paths.get(name)))) {
+                    checkAlongLine(numPoints, out);
+                } catch (IOException e) {
+                    Assertions.fail(e.getMessage());
+                }
+            } else {
+                checkAlongLine(numPoints, null);
+            }
+        }
+
+        /**
+         * Computes the values of the function along the straight line between
+         * {@link #startPoint} and {@link #optimum} and asserts that the value
+         * at the latter is smaller than at any other points along the line.
+         * <p>
+         * If the {@code output} stream is not {@code null}, two columns are
+         * printed:
+         * <ol>
+         *  <li>parameter in the {@code [0, 1]} interval (0 at {@link #startPoint}
+         *   and 1 at {@link #optimum}),</li>
+         *  <li>function value at {@code t * (optimum - startPoint)}.</li>
+         * </ol>
+         *
+         * @param numPoints Number of points to evaluate between {@link #start}
+         * and {@link #optimum}.
+         * @param output Output stream.
+         */
+        private void checkAlongLine(int numPoints,
+                                    PrintWriter output) {
+            final double delta = 1d / numPoints;
+
+            final int dim = start.length;
+            final double[] dir = new double[dim];
+            for (int i = 0; i < dim; i++) {
+                dir[i] = optimum[i] - start[i];
+            }
+
+            double[] minPoint = null;
+            double minValue = Double.POSITIVE_INFINITY;
+            int count = 0;
+            while (count <= numPoints) {
+                final double[] p = new double[dim];
+                final double t = count * delta;
+                for (int i = 0; i < dim; i++) {
+                    p[i] = start[i] + t * dir[i];
+                }
+
+                final double value = function.value(p);
+                if (value <= minValue) {
+                    minValue = value;
+                    minPoint = p;
+                }
+
+                if (output != null) {
+                    output.println(t + " " + value);
+                }
+
+                ++count;
+            }
+
+            final double tol = 1e-15;
+            Assertions.assertArrayEquals(optimum, minPoint, tol,
+                                         "Minimum: f(" + Arrays.toString(minPoint) + ")=" + minValue);
+        }
+
+        /**
+         * Generates a string suitable as a file name.
+         * <p>
+         * Brackets are removed; space, slash, "=" sign and comma
+         * characters are converted to underscores.
+         *
+         * @param f Function.
+         * @param start Start point.
+         * @param end End point.
+         * @return a string.
+         */
+        private static String createPlotBasename(MultivariateFunction f,
+                                                 double[] start,
+                                                 double[] end) {
+            final String s = f.toString() + "__" +
+                Arrays.toString(start) + "__" +
+                Arrays.toString(end) + ".dat";
+
+            final String repl = "_";
+            return s
+                .replaceAll("\\[", "")
+                .replaceAll("\\]", "")
+                .replaceAll("=", repl)
+                .replaceAll(",\\s+", repl)
+                .replaceAll(",", repl)
+                .replaceAll("\\s", repl)
+                .replaceAll("/", repl);
+        }
     }
 
     /**