example pennon structure to play with call penm=expen & problem=penlab(penm)
0001 % example pennon structure to play with 0002 % call penm=expen & problem=penlab(penm) 0003 function penm=expen() 0004 0005 penm = []; 0006 0007 % [optional] problem name and a comment (e.g. source) 0008 % just for logging 0009 penm.probname = 'Example Problem 1'; 0010 penm.comment = 'bla bla comment'; 0011 0012 %% [optional] userdata 0013 % will get always pass in and from any callback function, can be anything 0014 % if not set, an empty array will be used instead 0015 penm.userdata = []; 0016 0017 % [optional] option settings different from defaults 0018 penm.opts=[]; 0019 0020 %% define decision variables 0021 % number of (ordinary) decision variables 0022 % If the field is not present, Nx=0; lower/upper bounds for box constraints 0023 % will be ignored. 0024 penm.Nx = 7; 0025 % number of matrix variables, should be the same as length(Y) 0026 % If the field is not present, NY=0; thus Y{:}, bounds etc. will be ignored. 0027 penm.NY = 3; 0028 % cell array of length 'NY' with a nonzero pattern of each of the matrix 0029 % variables. Each matrix will be symmetrized and all its nonzeros in one 0030 % triangle will be considered as variables, the rest as constant zeros. 0031 % Whenever array Y{} is present in the callbacks, it will be symmetrized. 0032 % All (element-)variables will be counted with indicies starting with (Nx+1), 0033 % the order is Y{1}, Y{2}, ..., Y{NY} and in each matrix lower (symmetrized) 0034 % triangle column-wise. If any (derivative) callback needs derivatives 0035 % with respect to 'k' (k>Nx), it means it's one of the variables in one 0036 % of the matrices. A routine '...' can generate back the matrix and the exact 0037 % position of the variable ... 0038 penm.Y{1} = ones(3); 0039 penm.Y{2} = spones(sprandsym(5,0.3)); 0040 penm.Y{3} = spones(sprand(6,6,0.2)); 0041 0042 %% decision variables box constraints 0043 % box constraints (lower/upper bounds) on the variables, lbx <= x <= ubx 0044 % if lbx==-Inf, it is not considered; similarly if ubx=Inf so, e.g., 0045 % by setting lbx=-Inf, ubx=Inf the variable is unbounded. 0046 % length of each array should be Nx 0047 % if one or both are missing, 'x' is considered as unconstrained from that 0048 % side. Any ubx>lbx is considered as error. If lbx==ubx the variable will 0049 % be fixed and won't have further effect. 0050 penm.lbx = 0; 0051 %penm.lbx = [-Inf, -Inf, -1, 0, -3, -6, -77]; 0052 penm.ubx = [10, Inf, Inf, 4, 66, 0.1, Inf]; 0053 0054 % lower, upper bounds on Y variable elements? 0055 % if not present, unconstrained 0056 % penm.lbYx, ubYx ? or not at all? It can be always defined as one of the g() 0057 % constraints 0058 0059 % lower and upper bound on matrices Y (as matrix inequalities, i.e. eigenvals) 0060 % if fixed... what to do? Might even not have solution... 0061 % length NY 0062 penm.lbY = [0, -Inf, 1]; 0063 penm.ubY = [Inf, 0, 10]; 0064 0065 % [optional] box constraints on the elements of the matrix variables 0066 % only elements matchin patterns of Y{} will be taken into account 0067 % if the matrix is empty ([]) it is automatically considered as +/-Inf 0068 % accordingly 0069 penm.lbYx{1} = - magic(3); 0070 penm.ubYx{1} = magic(3); 0071 penm.lbYx{2} = sparse(5,5); 0072 penm.ubYx{3} = 100; 0073 0074 %% starting point 0075 % ideally feasible, might get adjusted, optional, if not set will be computed 0076 % somehow. With the matrices, it will accept only these nnz which where in 0077 % Y pattern. Symmetric or automatically lower triangle??? 0078 penm.xinit=rand(penm.Nx,1); 0079 %penm.Yinit{1} {2} {3}=....; 0080 0081 %% linear and nonlinear function constraints 0082 % nonlinear constraints, first NLN , then LIN 0083 penm.NgNLN = 2; 0084 penm.NgLIN = 1; 0085 0086 % nonlinear and linear matrix constraints 0087 penm.NANLN = 0; 0088 penm.NALIN = 1; 0089 0090 % lower/upper bounds ... equalities, must be defined at least on one side 0091 % (e.g. not unconstrained constraints ;-) 0092 penm.lbg = [-Inf, 0, 5]; 0093 penm.ubg = [0, Inf, 5]; 0094 penm.lbA = [0]; 0095 penm.ubA = [Inf]; 0096 0097 %% call back functions to evaluate objective function, function constraints 0098 % and matrix constraint and their derivatives. First go NLN then LIN. 0099 %penm.objfun = ... 0100 % [fx, userdata] = objfun(x,Y,userdata) % returns a number 0101 % [fdx, userdata] = objgrad(x,Y,userdata) % returns a (sparse) vector 0102 % w.r.t. all variables (even matrix ones) 0103 % objfun, objgrad, objhess 0104 % confun, congrad, conhess 0105 % mconfun, mcongrad, mconhess 0106 % alternatively objhess + conhess -> lagrhess 0107 0108 %[fx, userdata] = objfun(x,Y,userdata) % returns a number 0109 0110 %[fdx, userdata] = objgrad(x,Y,userdata) % returns a (possibly sparse) vector 0111 % w.r.t. all variables (even matrix ones), if objfun doesn't depend on Y 0112 % it can be just Nx long, otherwise Nx+NYnnz 0113 0114