Index: src/solver.rs
==================================================================
--- src/solver.rs
+++ src/solver.rs
@@ -70,10 +70,21 @@
         Parameter(msg: String) {
             description("Parameter error")
             display("Parameter error: {}", msg)
         }
 
+        /// The lower bound of a variable is larger than the upper bound.
+        InvalidBounds(lower: Real, upper: Real) {
+            description("invalid bounds")
+            display("Invalid bounds, lower:{} upper:{}", lower, upper)
+        }
+
+        /// The value of a variable is outside its bounds.
+        ViolatedBounds(lower: Real, upper: Real, value: Real) {
+            description("violated bounds")
+            display("Violated bounds, lower:{} upper:{} value:{}", lower, upper, value)
+        }
     }
 }
 
 
 /// Result type for solvers.
@@ -505,10 +516,11 @@
         let lb = self.problem.lower_bounds().map(|x| x.to_dense());
         let ub = self.problem.upper_bounds().map(|x| x.to_dense());
         for i in 0..self.cur_y.len() {
             let lb_i = lb.as_ref().map(|x| x[i]).unwrap_or(NEG_INFINITY);
             let ub_i = ub.as_ref().map(|x| x[i]).unwrap_or(INFINITY);
+            if lb_i > ub_i { return Err(Error::InvalidBounds(lb_i, ub_i)); }
             if self.cur_y[i] < lb_i {
                 self.cur_valid = false;
                 self.cur_y[i] = lb_i;
             } else if self.cur_y[i] > ub_i {
                 self.cur_valid = false;
@@ -567,11 +579,17 @@
 
         let mut newvars = Vec::with_capacity(updates.len());
         for u in updates {
             match u {
                 Update::AddVariable{lower, upper} => {
-                    newvars.push((lower, upper));
+                    if lower > upper {
+                        return Err(Error::InvalidBounds(lower, upper))
+                    }
+                    let value = if lower > 0.0 { lower }
+                    else if upper < 0.0 { upper }
+                    else { 0.0 };
+                    newvars.push((lower - value, upper - value));
                 },
             }
         }
 
         if !newvars.is_empty() {