QPROG/DQPROG (Single/Double precision)

       Solve a quadratic programming problem subject to linear equality/inequality 
       constraints. 
       
       Usage 
       CALL QPROG (NVAR, NCON, NEQ, A, LDAi,B, G, H, LDH, DIAG,
                   SOL, NACT, IACT, ALAMDA) 
                   
       Arguments 
       NVAR ― The numbcr ef variables. (Input) 
       NCON ― Thc number of linear constraints. (Input) 
       NEQ  ― The number of linear equality constraints. (Input) 
       A    ― NCON by NVAR matrix. (Input) 
               The matrix contains the equality contraints in thc first NEQ rows  
               followed by the inequality constraints. 
       LDA  ― Leading dimension of A exactly as specified in the dimension statement 
               of the calling program. (Input) 
       B    ― Vector of length NCON containing right-hand sides of the linear 
               constraints . (Input) 
       G    ― Vector of length NVAR containing the coefficients of the linear term of the 
               objective function. (Input) 
       H    ― NVAR by NVAR matrix containing the Hessian matrix of thc objective 
               function. (Input) 
               H should be symmetric positive definite; if H is not positive definite, the 
               algorithm attempts to solve the QP problem with H replaced by a H + DIAG * I 
               such that H + DIAG * I is positive definite. See Comment 3. 
       LDH  ― Leading dimension of H exactly as specified in the dimension statement 
               of the calling program. (Input) 
       DIAG ― Scalar equal to thc multiple of the identity matrix added to H to give a 
               positive definite matrix. (Output) 
       SOL  ― Vector of length NVAR containing solution. (Output) 
       NACT ― Final number of active constraints. (Output) 
       LACT ― Vector of length NVAR oontaining thc indices of the final active 
               constraints in the first NACT positions. (Output) 
       ALAMDA ― Vector of length NVAR containing the Lagrange multiplier 
               estimatcs of the final active constraints in tbe first NACT positions. (Output) 

       Comments 
       1. Automatic workspace usage is 
          QPROG (3 * NVAR ** 2 + 11 * NVAR)/2 + NCON units, or 
          DQPROG (3 * NVAR ** + 2 + 11 ＊ NVAR) + 2 ＊NCON units. 
          
          Workspacc may be explicitly provided,  if desired,  by use of 
          Q2ROG/DQ2ROG. Thc reference is 
          
          CALL Q2ROG  (NVAR, NCON, NEQ, A, LDA, B, G, H, LDH, 
                       DIAG, SOL, NACT, IACT, ALAMDA, WK) 
                       
          Thc additional argument is 
          WK ― Work vector of length(3 * NVAR**2 + 11 * NVAR)/2 + NCON. 
       2. Informational errors
          Type  Code
           3     1    Due to the effect of computer rounding error, a
                      cbange in the variables fail to improvc the objective 
                      function value ; usually the solution is close to
                      optimum.
           4     2    The system of equations is inconsistent. There is no
                      solution.
       3. If a perturbation of H, H + DIAG * I, was used in the QP problem, then
          H + DIAG * I should  also be used in the definition of the Lagrange 
          multipliers.

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