SOCP docu #192

Section in the Modeling Guide

Author: glebbelov

doc/rst/modeling-expressions.rst

@@ -384,11 +384,43 @@ Certain nonlinear solvers, notably Knitro, handle complementarity constraints na
           cost[j] - sum {i in PROD} Price[i] * io[i,j];
 
 
-Nonlinear operators and functions
+
+Set membership operator
 **********************************
 
+- var *var-name* in *set-expr* ;
+    Defines a variable that must be a member of a specified AMPL set,
+    as given by the expression *set-expr*. All members of the set must be numbers.
+
+This is the simplest use of ``in`` to restrict the domain of a set; more
+generally, the *in set-expr* phrase may appear in any ``var`` definition
+that does not contain an *=* phrase.
+
+Before sending a problem to the solver interface, AMPL converts variable
+definitions of this kind to alternative definitions that do not use the
+``in`` operator. This may involve the definition of auxiliary binary
+variables and additional constraints. In the usual case where *set-expr*
+is a finite set, AMPL also defines suffixes ``.sos`` and ``.sosref`` which
+can be used by the solver interface to recognize variables and constraints
+that have been created to implement an ``in`` operator, and to support
+solvers that handle arbitrary variable domains by means of
+"special ordered sets of type 1". It is also possible to specify sets
+that contain continuous intervals -- and hence are infinite -- by using
+the AMPL expression *interval[expr1,expr2]*.
+
+.. code-block:: ampl
+
+    var Buy {f in FOODS} in {0,10,30,45,55};
+
+.. code-block:: ampl
+
+    var Ship {(i,j) in ARCS}
+       in {0} union interval[min_ship,capacity[i,j]];
+
+
+
 Quadratic and power operators
-$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
+**********************************
 
 - *expr1* * *expr2*
     *expr-valued:* Multiplication of *expr1* and *expr2*.
@@ -431,8 +463,34 @@ previously described. For example:
           c[i] * x[i] / (40 * b[i] * sum {j in J} x[j] / b[j]);
 
 
+Second-order cone programming (SOCP)
+**************************************
+
+Some solvers can handle SOCP constraints: Mosek, Gurobi, COPT.
+SOCP constraints are recognized by MP drivers from their algebraic
+representations. Examples:
+
+- Standard SOC:
+
+  .. code-block:: ampl
+
+    x[0] >= sqrt(x[1]^2 + … + x[n]^2);
+    -5*x[0]^2 <= -x[1]^2 - … - x[n]^2,     where x[0] >= 0;
+    0.04 >= abs(x[1]);
+
+- Rotated SOC  (where x[0], x[1] >= 0):
+
+  .. code-block:: ampl
+
+    3*sqrt(5*x[0]*x[1]) >= 15*sqrt(10*x[2]^2 + … + 80*x[n]^2);
+    2*x[0]*x[1] >= x[2]^2 + … + x[n]^2;
+
+*Note:* Option `cvt:socp=0` results in second-order conic
+constraints being passed to the solver as quadratics.
+
+
 General nonlinear functions
-$$$$$$$$$$$$$$$$$$$$$$$$$$$
+**********************************
 
 - log (*expr*), log10 (*expr*)
     *expr-valued:* The natural and base-10 logarithms of *expr*.
@@ -504,23 +562,3 @@ specifies 12 pieces for approximating the sin, cos, and exp functions in that ob
        x[1]^2 - 12*x[1] + 11 + 10*cos(pi*x[1]/2) +
           8*sin(pi*5*x[1]) - exp(-(x[2]-.5)^2/2)/sqrt(5);
 
-
-Set membership operator
-**********************************
-
-- var *var-name* in *set-expr* ;
-    Defines a variable that must be a member of a specified AMPL set, as given by the expression *set-expr*. All members of the set must be numbers.
-
-This is the simplest use of ``in`` to restrict the domain of a set; more generally, the *in set-expr* phrase may appear in any ``var`` definition that does not contain an *=* phrase.
-
-Before sending a problem to the solver interface, AMPL converts variable definitions of this kind to alternative definitions that do not use the ``in`` operator. This may involve the definition of auxiliary binary variables and additional constraints. In the usual case where *set-expr* is a finite set, AMPL also defines suffixes ``.sos`` and ``.sosref`` which can be used by the solver interface to recognize variables and constraints that have been created to implement an ``in`` operator, and to support solvers that handle arbitrary variable domains by means of "special ordered sets of type 1". It is also possible to specify sets that contain continuous intervals -- and hence are infinite -- by using the AMPL expression *interval[expr1,expr2]*.
-
-.. code-block:: ampl
-
-    var Buy {f in FOODS} in {0,10,30,45,55};
-
-.. code-block:: ampl
-
-    var Ship {(i,j) in ARCS}
-       in {0} union interval[min_ship,capacity[i,j]];
-

include/mp/flat/converter.h

@@ -891,8 +891,10 @@ class FlatConverter :
 		if (ModelAPIAcceptsQuadraticCones())
 			GetEnv().AddOption("cvt:socp passsocp socp",
 												 ModelAPIAcceptsQuadraticCones()>1 ?
-													 "0/1*: Recognize quadratic cones." :
-													 "0*/1: Recognize quadratic cones.",
+                           "0/1*: Recognize quadratic cones vs passing them "
+                           "as pure quadratic constraints." :
+                           "0*/1: Recognize quadratic cones vs passing them "
+                           "as pure quadratic constraints.",
 					options_.passSOCPCones_, 0, 1);
 		options_.passSOCPCones_ = ModelAPIAcceptsQuadraticCones()>1;
 		GetEnv().AddOption("alg:relax relax",

solvers/copt/CHANGES.copt.md

@@ -2,6 +2,13 @@ Summary of recent updates to COPT for AMPL
 ==========================================
 
 
+## unreleased
+- Recognition of second-order conic constraints
+  from algebraic representations and conversion into
+  quadratic constraints; COPT appears to recognize
+  second-order cones from quadratics.
+
+
 ## 20230207
 - *Changes in the MP library*
 - Updated to Copt 6.0.4, which includes bugfixes

test/end2end/scripts/python/Solver.py

@@ -741,7 +741,12 @@ def _getAMPLOptionsName(self):
 
     def __init__(self, exeName, timeout=None, nthreads=None, otherOptions=None):
         stags = {ModelTags.continuous, ModelTags.integer, ModelTags.binary,
-                 ModelTags.quadratic, ModelTags.quadratic_obj}
+                 ModelTags.quadratic, ModelTags.quadratic_obj,
+
+                 ModelTags.socp,      ## MP transforms cones to quadratics
+                 ModelTags.socp_hard_to_recognize
+
+                 }
         super().__init__(exeName, timeout, nthreads, otherOptions, stags)