feat: allow defining initial values for individual variables

Author: KnorpelSenf

src/variable.rs

@@ -118,6 +118,7 @@ impl FormatWithVars for Variable {
 pub struct VariableDefinition {
     pub(crate) min: f64,
     pub(crate) max: f64,
+    pub(crate) initial: Option<f64>,
     pub(crate) name: String,
     pub(crate) is_integer: bool,
 }
@@ -128,6 +129,7 @@ impl VariableDefinition {
         VariableDefinition {
             min: f64::NEG_INFINITY,
             max: f64::INFINITY,
+            initial: None,
             name: String::new(),
             is_integer: false,
         }
@@ -177,6 +179,27 @@ impl VariableDefinition {
         self
     }
 
+    /// Set the initial value of the variable. This may help the solver to find a solution significantly faster.
+    ///
+    /// **Warning**: not all solvers support integer variables.
+    /// Refer to the documentation of the solver you are using.
+    ///
+    /// ```
+    /// # use good_lp::{ProblemVariables, variable, default_solver, SolverModel, Solution};
+    /// let mut problem = ProblemVariables::new();
+    /// let x = problem.add(variable().max(3).initial(3));
+    /// let y = problem.add(variable().max(5).initial(5));
+    /// if cfg!(not(any(feature="clarabel"))) {
+    ///     let solution = problem.maximise(x + y).using(default_solver).solve().unwrap();
+    ///     assert_eq!(solution.value(x), 3.);
+    ///     assert_eq!(solution.value(y), 5.);
+    /// }
+    /// ```
+    pub fn initial<N: Into<f64>>(mut self, value: N) -> Self {
+        self.initial = Some(value.into());
+        self
+    }
+
     /// Set the name of the variable. This is useful in particular when displaying the problem
     /// for debugging purposes.
     ///