\$title Test inequalities with infinite bounds (MCP09,SEQ=440) \$ontext This started as an example to show equivalent complementarity models, one using positive vars and the other using "mixed bounds", i.e arbitrary lower and upper bounds. Put another way, this compares/contrasts NCP and MCP. There should be nothing lost in the MCP formulation, with a gain in clarity/maintainability. This example turned up an issue when we use infinite bounds on inequalities for complementarity problems. For this example, think of the KKT system for the optimization problem min sqr(x-c) s.t. L <= x <= U Contributor: Steve Dirkse, March 2009 \$offtext scalars c / 3 / L, U; variable z 'arbitrary bounded'; positive variable x, loSlack, upSlack; * if we have L >= 0 we can let x be >= 0 equations f 'MCP function' g 'NCP function' loBound, upBound; ; f.. 2*(z-c) =N= 0; g.. 2*(x-c) - loSlack + upSlack =G= 0; loBound.. x =G= L; upBound.. U =G= x; model ncp 'NCP version' / g.x, loBound.loSlack, upBound.upSlack /; model m 'MCP version' / f.z /; set cases / c1 * c7 / loup / L, U /; table bnds(cases, loup) L U c1 4 5 c2 1 2 c3 2 4 c4 4 1e4 c5 -1e4 2 c6 4 inf c7 -inf 2 ; parameter report (cases,*,*) diff(cases,*); alias(v,*); loop {cases, L = bnds(cases,'L'); U = bnds(cases,'U'); z.lo = L; z.up = U; solve m using mcp; abort\$[m.modelstat <> %modelstat.Optimal%] 'bad modelstat solving MCP'; abort\$[m.solvestat <> %solvestat.NormalCompletion%] 'bad solvestat solving MCP'; report(cases,'mcp','xLev') = z.l; report(cases,'mcp','loSlack') = max( z.m,0); report(cases,'mcp','upSlack') = max(-z.m,0); solve ncp using mcp; abort\$[ncp.modelstat <> %modelstat.Optimal%] 'bad modelstat solving NCP'; abort\$[ncp.solvestat <> %solvestat.NormalCompletion%] 'bad solvestat solving NCP'; report(cases,'ncp','xLev') = x.l; report(cases,'ncp','loSlack') = loSlack.l; report(cases,'ncp','upSlack') = upSlack.l; }; diff(cases,v) = abs(report(cases,'ncp',v) - report(cases,'mcp',v)); display bnds, report, diff; abort\$[smax{(cases,v), diff(cases,v)} > 1e-6] 'different results';