eval_nln_constraint_hess

EVAL_NLN_CONSTRAINT_HESS  Builds and returns Hessian of nonlinear constraints.
   D2G = OM.EVAL_NLN_CONSTRAINT_HESS(X, LAM, ISEQ)
   Builds the Hessian of the full set of nonlinear equality or inequality
   constraints for given values of the optimization vector X and dual
   variables LAM, based on constraints added by ADD_NLN_CONSTRAINT.

       g(X) = 0
       h(X) <= 0

   Example:
       d2G = om.eval_nln_constraint_hess(x, lam, 1)
       d2H = om.eval_nln_constraint_hess(x, lam, 0)

   See also OPT_MODEL, ADD_NLN_CONSTRAINT, EVAL_NLN_CONSTRAINT.

0001 function d2G = eval_nln_constraint_hess(om, x, lam, iseq)
0002 %EVAL_NLN_CONSTRAINT_HESS  Builds and returns Hessian of nonlinear constraints.
0003 %   D2G = OM.EVAL_NLN_CONSTRAINT_HESS(X, LAM, ISEQ)
0004 %   Builds the Hessian of the full set of nonlinear equality or inequality
0005 %   constraints for given values of the optimization vector X and dual
0006 %   variables LAM, based on constraints added by ADD_NLN_CONSTRAINT.
0007 %
0008 %       g(X) = 0
0009 %       h(X) <= 0
0010 %
0011 %   Example:
0012 %       d2G = om.eval_nln_constraint_hess(x, lam, 1)
0013 %       d2H = om.eval_nln_constraint_hess(x, lam, 0)
0014 %
0015 %   See also OPT_MODEL, ADD_NLN_CONSTRAINT, EVAL_NLN_CONSTRAINT.
0016 
0017 %   MATPOWER
0018 %   Copyright (c) 2008-2017, Power Systems Engineering Research Center (PSERC)
0019 %   by Ray Zimmerman, PSERC Cornell
0020 %
0021 %   This file is part of MATPOWER.
0022 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0023 %   See https://matpower.org for more info.
0024 
0025 %% get constraint type
0026 if iseq         %% equality constraints
0027     om_nlx = om.nle;
0028 else            %% inequality constraints
0029     om_nlx = om.nli;
0030 end
0031 
0032 %% initialize d2G (use transpose for speed on older versions of MATLAB)
0033 d2Gt = sparse(om.var.N, om.var.N);
0034 
0035 %% calls to substruct() are relatively expensive, so we pre-build the
0036 %% structs for addressing cell and numeric array fields, updating only
0037 %% the subscripts before use
0038 sc = struct('type', {'.', '{}'}, 'subs', {'', 1});  %% cell array field
0039 sn = sc; sn(2).type = '()';                         %% num array field
0040 
0041 %% fill in each piece
0042 for k = 1:om_nlx.NS
0043     name = om_nlx.order(k).name;
0044     idx  = om_nlx.order(k).idx;
0045     if isempty(idx)
0046         if ~isfield(om_nlx.data.hess, name)
0047             continue;   %% skip, there is no function handle stored here,
0048                         %% the function value for this named set was included
0049                         %% in the value computed by a previous named set
0050         end
0051         N = om_nlx.idx.N.(name);    %% number of constraint functions
0052                                     %% evaluated for this named set
0053         if isfield(om_nlx.data.include, name)
0054             N = N + sum(om_nlx.data.include.(name).N);
0055         end
0056     else
0057         % (calls to substruct() are relatively expensive ...
0058         % sn = substruct('.', name, '()', idx);
0059         % sc = substruct('.', name, '{}', idx);
0060         % ... so replace them with these more efficient lines)
0061         sn(1).subs = name;
0062         sn(2).subs = idx;
0063         sc(1).subs = name;
0064         sc(2).subs = idx;
0065         N = subsref(om_nlx.idx.N, sn);
0066     end
0067     if N                                %% non-zero number of rows
0068         if isempty(idx)
0069             d2G_fcn = om_nlx.data.hess.(name);  %% Hessian fcn for kth constraint set
0070             i1 = om_nlx.idx.i1.(name);          %% starting row index
0071             iN = i1 + N - 1;                    %% ending row index
0072             vs = om_nlx.data.vs.(name);         %% var sets
0073         else
0074             d2G_fcn = subsref(om_nlx.data.hess, sc);  %% Hessian fcn for kth constraint set
0075             i1 = subsref(om_nlx.idx.i1, sn);    %% starting row index
0076             iN = subsref(om_nlx.idx.iN, sn);    %% ending row index
0077             vs = subsref(om_nlx.data.vs, sc);   %% var sets
0078         end
0079         xx = om.varsets_x(x, vs);
0080         d2Gk = d2G_fcn(xx, lam(i1:iN));     %% evaluate kth Hessian
0081         
0082         nk = size(d2Gk, 2);
0083         if isempty(vs)          %% all rows of x
0084             if nk == om.var.N
0085                 d2Gkt_full = d2Gk';
0086             else                %% must have added vars since adding
0087                                 %% this constraint set
0088                 d2Gk_all_cols = sparse(nk, om.var.N);
0089                 d2Gk_all_cols(:, 1:nk) = d2Gk;
0090                 d2Gkt_full = sparse(om.var.N, om.var.N);
0091                 d2Gkt_full(:, 1:nk) = d2Gk_all_cols';
0092             end
0093         else                    %% selected rows of x
0094             jj = om.varsets_idx(vs);    %% indices for var set
0095             d2Gk_all_cols = sparse(nk, om.var.N);
0096             d2Gk_all_cols(:, jj) = d2Gk;
0097             d2Gkt_full = sparse(om.var.N, om.var.N);
0098             d2Gkt_full(:, jj) = d2Gk_all_cols';
0099         end
0100         d2Gt = d2Gt + d2Gkt_full;
0101     end
0102 end
0103 d2G = d2Gt';