adding model-based opt facility

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/math/simplex/model_based_opt.h

@@ -0,0 +1,102 @@
+/*++
+Copyright (c) 2016 Microsoft Corporation
+
+Module Name:
+
+    model_based_opt.h
+
+Abstract:
+
+    Model-based optimization for linear real arithmetic.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2016-27-4
+
+Revision History:
+
+
+--*/
+
+#ifndef __MODEL_BASED_OPT_H__
+#define __MODEL_BASED_OPT_H__
+
+#include "util.h"
+#include "rational.h"
+
+namespace opt {
+   
+    enum ineq_type {
+        t_eq,
+        t_lt,
+        t_le
+    };
+
+    enum bound_type {
+        unbounded,
+        strict,
+        non_strict
+    };
+    
+    class model_based_opt {
+    public:
+        struct var {
+            unsigned m_id;
+            rational m_coeff;
+            var(unsigned id, rational const& c): m_id(id), m_coeff(c) {}
+        };
+    private:
+        struct row {
+            vector<var> m_vars;         // variables with coefficients
+            rational    m_coeff;        // constant in inequality
+            ineq_type   m_type;         // inequality type
+            rational    m_value;        // value of m_vars + m_coeff under interpretation of m_var2value.
+            bool        m_alive;        // rows can be marked dead if they have been processed.
+        };
+        vector<row>             m_rows;
+        vector<unsigned_vector> m_var2row_ids;
+        vector<rational>        m_var2value;
+        row                     m_objective;
+        vector<var>             m_new_vars;
+        
+        bool invariant();
+        bool invariant(row const& r);
+        
+
+        bool find_bound(unsigned x, unsigned& bound_index, unsigned_vector& other, bool is_pos);
+        
+        rational get_coefficient(unsigned row_id, unsigned var_id);
+
+        bool resolve(unsigned row_id1, rational const& a1, unsigned row_id2, unsigned x);
+
+        void multiply(rational const& c, unsigned row_id);
+
+        void add(unsigned row_id1, unsigned row_id2);
+
+    public:
+
+        // add a fresh variable with value 'value'.
+        unsigned add_var(rational const& value);
+
+        // add a constraint. We assume that the constraint is 
+        // satisfied under the values provided to the variables.
+        void add_constraint(vector<var> const& coeffs, rational const& c, ineq_type r);
+
+        // Set the objective function (linear).
+        void set_objective(vector<var> const& coeffs, rational const& c);
+
+        // find a maximal value for the objective function over the current values.
+        // in other words, the returned maximal value may not be globally optimal,
+        // but the current evaluation of variables are used to select a local
+        // optimal.
+        bound_type maximize(rational& value);
+
+
+        void display(std::ostream& out) const;
+        void display(std::ostream& out, row const& r) const;
+
+    };
+
+}
+
+#endif