Update docs for rotated SOC and exp cone

docs/source/changelog.md

@@ -1,6 +1,7 @@
 # Changelog
 
 ## Unreleased change
+- Add rotated second-order cone and exponential cone support for COPT and Mosek
 
 ## 0.2.5
 - Fix `add_linear_constraint` of HiGHS optimizer to consider the constant term in expression correctly

docs/source/constraint.md

@@ -115,12 +115,44 @@ vars = [model.add_variable() for i in range(N)]
 con = model.add_second_order_cone_constraint(vars)
 ```
 
-```{py:function} model.add_second_order_cone_constraint(variables, [name=""])
+Some optimizers (COPT, Mosek) support another form of second-order cone constraint called as rotated second-order cone constraint, which is defined as:
+
+$$
+variables=(t_{1},t_{2},x) \in \mathbb{R}^{N} : 2 t_1 t_2 \ge \lVert x \rVert_2^2
+$$
+
+```{py:function} model.add_second_order_cone_constraint(variables, [name="", rotated=False])
+
+add a second order cone constraint to the model
+
+:param variables: the variables of the constraint, can be a list of variables
+:param str name: the name of the constraint, optional
+:param bool rotated: whether the constraint is a rotated second-order cone constraint, optional
+:return: the handle of the constraint
+```
+
+## Exponential Cone Constraint
+It is defined as:
+
+$$
+variables=(t,s,r) \in \mathbb{R}^{3} : t \ge s \exp(\frac{r}{s}), s \ge 0
+$$
+
+The dual form is:
+
+$$
+variables=(t,s,r) \in \mathbb{R}^{3} : t \ge -r \exp(\frac{s}{r} - 1), r \le 0
+$$
+
+Currently, only COPT(after 7.1.4), Mosek support exponential cone constraint. It can be added to the model using the `add_exp_cone_constraint` method of the `Model` class.
+
+```{py:function} model.add_exp_cone_constraint(variables, [name="", dual=False])
 
 add a second order cone constraint to the model
 
 :param variables: the variables of the constraint, can be a list of variables
 :param str name: the name of the constraint, optional
+:param bool dual: whether the constraint is dual form of exponential cone, optional
 :return: the handle of the constraint
 ```
 

docs/source/copt.md

@@ -33,6 +33,8 @@ model = copt.Model(env)
     - ✅
 *   - <project:#model.add_second_order_cone_constraint>
     - ✅
+*   - <project:#model.add_exp_cone_constraint>
+    - ✅
 *   - <project:#model.add_sos_constraint>
     - ✅
 

docs/source/mosek.md

@@ -33,6 +33,8 @@ model = mosek.Model(env)
     - ✅
 *   - <project:#model.add_second_order_cone_constraint>
     - ✅
+*   - <project:#model.add_exp_cone_constraint>
+    - ✅
 *   - <project:#model.add_sos_constraint>
     - ❌