Module qps_cplex

Quadratic Program Solver based on CPLEX.

A wrapper function providing a PYPOWER standardized interface for using cplexqp or cplexlp to solve the following QP (quadratic programming) problem:

   min 1/2 X'*H*x + c'*x
    x

subject to:

   l <= A*x <= u       (linear constraints)
   xmin <= x <= xmax   (variable bounds)

Inputs (all optional except H, c, A and l):

• H : matrix (possibly sparse) of quadratic cost coefficients
• c : vector of linear cost coefficients
• A, l, u : define the optional linear constraints. Default values for the elements of L and U are -Inf and Inf, respectively.
• xmin, xmax : optional lower and upper bounds on the x variables, defaults are -Inf and Inf, respectively.
• x0 : optional starting value of optimization vector x
• opt : optional options structure with the following fields, all of which are also optional (default values shown in parentheses)
  • verbose (0) - controls level of progress output displayed
    • 0 = no progress output
    • 1 = some progress output
    • 2 = verbose progress output
  • cplex_opt - options dict for CPLEX, value in verbose overrides these options
• problem : The inputs can alternatively be supplied in a single problem dict with fields corresponding to the input arguments described above: H, c, A, l, u, xmin, xmax, x0, opt

Outputs:

• x : solution vector
• f : final objective function value
• exitflag : CPLEXQP/CPLEXLP exit flag (see cplexqp and cplexlp documentation for details)
• output : CPLEXQP/CPLEXLP output dict (see cplexqp and cplexlp documentation for details)
• lmbda : dict containing the Langrange and Kuhn-Tucker multipliers on the constraints, with fields:
  • mu_l - lower (left-hand) limit on linear constraints
  • mu_u - upper (right-hand) limit on linear constraints
  • lower - lower bound on optimization variables
  • upper - upper bound on optimization variables