Identify squared linear sums as quadratic with generate_standard_repn

[johwiebe]

Fixes #1287

Summary/Motivation:

generate_standard_repn should recognize the square of a linear sum (x_1 + x_2 + ... + x_n)**2 as a quadratic when quadratic=True. It currently returns a nonlinear expression if the linear sum has more than one term. This leads, e.g., to issues when trying to solve a model with a quadratic constraint of this form with Gurobi.

Note that there is a test case which asks for this behavior for expression e = (m.a + m.b)**2:

pyomo/pyomo/repn/tests/test_standard.py

Lines 3141 to 3157 in 7920516

	rep = generate_standard_repn(e, compute_values=False, quadratic=True)
	#
	self.assertFalse( rep.is_fixed() )
	self.assertEqual( rep.polynomial_degree(), None )
	self.assertFalse( rep.is_constant() )
	self.assertFalse( rep.is_linear() )
	self.assertFalse( rep.is_quadratic() )
	self.assertTrue( rep.is_nonlinear() )
	#
	self.assertTrue(len(rep.linear_vars) == 0)
	self.assertTrue(len(rep.linear_coefs) == 0)
	self.assertTrue(len(rep.quadratic_vars) == 0)
	self.assertTrue(len(rep.quadratic_coefs) == 0)
	self.assertFalse(rep.nonlinear_expr is None)
	self.assertTrue(len(rep.nonlinear_vars) == 2)
	baseline = { }
	self.assertEqual(baseline, repn_to_dict(rep))

Am I missing a reason why this behavior might be wanted?

Changes proposed in this PR:

• _collect_pow returns a quadratic expression for any PowExpression with linear base and exponent 2. The underlying logic is:
  (sum_i x_i)**2 = sum_i sum_j x_i*x_j = sum_i x_i**2 + 2*sum_i sum_{j<i} x_i*x_j
• Modifies a test case for expression (m.a + m.b)**2 which currently expects generate_standard_repn to return a nonlinear expression.
• Adds a test case for expression (linear sum)**2 with more than two variables.

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[codecov]

Codecov Report

Merging #1493 into master will increase coverage by 0.02%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1493      +/-   ##
==========================================
+ Coverage   72.35%   72.38%   +0.02%     
==========================================
  Files         608      608              
  Lines       85595    85642      +47     
==========================================
+ Hits        61933    61991      +58     
+ Misses      23662    23651      -11     

Impacted Files	Coverage Δ
pyomo/repn/standard_repn.py	92.97% <100.00%> (+0.06%)	⬆️
pyomo/pysp/scenariotree/tree_structure.py	83.57% <0.00%> (-0.22%)	⬇️
pyomo/util/check_units.py	94.56% <0.00%> (+2.40%)	⬆️
pyomo/solvers/plugins/solvers/BARON.py	81.53% <0.00%> (+2.43%)	⬆️
pyomo/contrib/gdpopt/nlp_solve.py	74.91% <0.00%> (+2.60%)	⬆️

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[jsiirola]

I think this is OK to merge. The tests highlight a nondeterminism in the internal Results data structures, but resolving that is beyond the scope of this PR and I believe should be dealt with elsewhere (see #1073 and the solver-rewrite).

[jsiirola]

Note that this is inherently nondeterministic. Unfortunately, this is a flaw in the current Results data structures. It will be resolved n an upcoming rewrite of generate_standard_repn (see #1073 and the draft implementation on the solver-rewrite branch)

[jsiirola]

I stand corrected. @carldlaird pointed out to me that this can be made deterministic relatively easily. Expect a PR from him that will resolve this and then we can merge.