SolverResult KojimaSolver::solve(const LCP & lcp,
vec & x,
vec & y) const{
superlu_opts opts;
opts.equilibrate = true;
opts.permutation = superlu_opts::COLAMD;
opts.refine = superlu_opts::REF_SINGLE;
vec q = lcp.q;
sp_mat M = lcp.M + regularizer * speye(size(lcp.M));
uint N = q.n_elem;
assert(N == x.n_elem);
assert(N == y.n_elem);
// Figure out what is free (-inf,inf)
// and what is bound to be non-negative [0,inf)
bvec free_vars = lcp.free_vars;
uvec bound_idx = find(0 == free_vars);
uvec free_idx = find(1 == free_vars);
assert(N == bound_idx.n_elem + free_idx.n_elem);
uint NB = bound_idx.n_elem; // number of bound vars
uint NF = free_idx.n_elem; // number of free vars
/*
In what follows, the primal variables x are partitioned into
free variables and bound variables x = [f;b]'
Likewise, the dual variables are partitioned into y = [0,s]'
*/
/* The Newton system:
[M_ff M_fb 0][df] [M_f x + q_f]
[M_bf M_bb -I][db] + [M_b x + q_b - s]
[0 S B][dv] [u1 + VBe]
Where "M_ff" is the free-free block
Overwrite the S,B diagonals every iteration*/
// Split M matrix into blocks based on free and bound indicies
block_sp_mat M_part = sp_partition(M,free_idx,bound_idx);
sp_mat M_recon = block_mat(M_part);
assert(PRETTY_SMALL > norm(M_recon - M));
vec qf = q(free_idx);
vec qb = q(bound_idx);
vec b = x(bound_idx);
vec f = x(free_idx);
vec s = y(bound_idx);
// Build the Newton matrix
vector<vector<sp_mat>> block_G;
block_G.push_back(block_sp_vec{sp_mat(),sp_mat(),sp_mat(NB,NB)});
block_G.push_back(block_sp_vec{-M_part[0][0],-M_part[0][1],sp_mat()});
block_G.push_back(block_sp_vec{-M_part[1][0],-M_part[1][1],speye(NB,NB)});
// Start iteration
double mean_comp, steplen;
double sigma = initial_sigma;
uint iter;
for(iter = 0; iter < max_iter; iter++){
if(verbose or iter_verbose)
cout << "---Iteration " << iter << "---" << endl;
assert(all(0 == y(free_idx)));
// Mean complementarity
mean_comp = dot(b,s) / (double) NB;
if(mean_comp < comp_thresh)
break;
block_G[0][1] = spdiag(s);
block_G[0][2] = spdiag(b);
sp_mat G = block_mat(block_G);
assert(size(N + NB,N + NB) == size(G));
// Form RHS from residual and complementarity
vec h = vec(N + NB);
vec res_f = M_part[0][0]*f + M_part[0][1]*b + qf;
vec res_b = M_part[1][0]*f + M_part[1][1]*b + qb - s;
h.head(NB) = sigma * mean_comp - b % s;
h.subvec(NB,size(res_f)) = res_f;
h.tail(NB) = res_b;
//Archiver arch;
//arch.add_sp_mat("G",G);
//arch.add_vec("h",h);
//arch.write("test.sys");
// Solve and extract directions
vec dir = spsolve(G,h,"superlu",opts);
assert((N+NB) == dir.n_elem);
vec df = dir.head(NF);
vec db = dir.subvec(NF,N-1);
assert(NB == db.n_elem);
vec ds = dir.tail(NB);
vec dir_recon = join_vert(df,join_vert(db,ds));
assert(PRETTY_SMALL > norm(dir_recon-dir));
steplen = steplen_heuristic(b,s,db,ds,0.9);
sigma = sigma_heuristic(sigma,steplen);
f += steplen * df;
b += steplen * db;
s += steplen * ds;
if(verbose){
double res = norm(join_vert(res_f,res_b));
cout <<"\t Mean complementarity: " << mean_comp
<<"\n\t Residual norm: " << res
<<"\n\t |df|: " << norm(df)
<<"\n\t |db|: " << norm(db)
<<"\n\t |ds|: " << norm(ds)
<<"\n\t Step length: " << steplen
<<"\n\t Centering sigma: " << sigma << endl;
}
}
if(verbose){
cout << "Finished"
<<"\n\t Final mean complementarity: " << mean_comp << endl;
}
x(free_idx) = f;
x(bound_idx) = b;
y(free_idx).fill(0);
y(bound_idx) = s;
return SolverResult(x,y,iter);
}
SolverResult MultiSolver::solveNaive(MultiSolverInput &input)
{
Vector location = NLLeastSquareSolver(&input);
return SolverResult(location, input.data);
}
SolverResult ProjectiveSolver::solve(const PLCP & plcp,
vec & x,
vec & y,
vec & w) const{
sp_mat P = plcp.P;
sp_mat U = plcp.U;
vec q = plcp.q;
uint N = P.n_rows;
uint K = P.n_cols;
assert(size(P.t()) == size(U));
bvec free_vars = plcp.free_vars;
uvec bound_idx = find(0 == free_vars);
uvec free_idx = find(1 == free_vars);
assert(N == bound_idx.n_elem + free_idx.n_elem);
uint NB = bound_idx.n_elem; // number of bound vars
uint NF = free_idx.n_elem; // number of free vars
assert(NF == accu(conv_to<uvec>::from(free_vars)));
assert(N == x.n_elem);
assert(N == y.n_elem);
assert(K == w.n_elem);
assert(ALMOST_ZERO > norm(y(free_idx)));
if(verbose)
cout << "Free variables: \t" << NF << endl
<< "Non-neg variables:\t" << NB << endl;
sp_mat J = join_vert(sp_mat(NF,NB),speye(NB,NB));
assert(size(N,NB) == size(J));
assert(PRETTY_SMALL > norm(y(free_idx)));
if(verbose)
cout << "Forming pre-computed products..." << endl;
mat PtP = mat(P.t() * P);
assert(size(K,K) == size(PtP));
mat PtPU = PtP*U;
assert(size(K,N) == size(PtPU));
mat Pt_PtPU = P.t() - PtPU;
assert(size(K,N) == size(Pt_PtPU));
mat PtPUP = PtPU * P;
assert(size(K,K) == size(PtPUP));
vec Ptq = P.t() * q;
if(verbose)
cout << "Done..." << endl;
double sigma = initial_sigma;
uint iter;
double mean_comp;
for(iter = 0; iter < max_iter; iter++){
if(verbose or iter_verbose)
cout << "---Iteration " << iter << "---" << endl;
// Mean complementarity
vec s = y(bound_idx);
vec b = x(bound_idx);
mean_comp = dot(s,b) / (double) NB;
if(mean_comp < comp_thresh)
break;
// Generate reduced Netwon system
mat C = s+b;
vec g = sigma * mean_comp - s % b;
assert(NB == g.n_elem);
// NB: A,G,and h have opposite sign from python version
mat A = Pt_PtPU * J * spdiag(1.0 / C);
assert(size(K,NB) == size(A));
mat G = PtPUP + (A * spdiag(s)) * J.t() * P;
assert(size(K,K) == size(G));
vec Ptr = P.t() * (J * s) - PtPU*x - Ptq;
vec h = Ptr + A*g;
assert(K == h.n_elem);
// Options don't make much difference
vec dw = arma::solve(G+1e-15*eye(K,K),h,
solve_opts::equilibrate);
assert(K == dw.n_elem);
// Recover dy
vec Pdw = P * dw;
vec JtPdw = J.t() * Pdw;
assert(NB == JtPdw.n_elem);
vec ds = (g - s % JtPdw) / C;
assert(NB == ds.n_elem);
// Recover dx
vec dx = (J * ds) + (Pdw);
assert(N == dx.n_elem);
double steplen = steplen_heuristic(x(bound_idx),s,dx(bound_idx),ds,0.9);
sigma = sigma_heuristic(sigma,steplen);
x += steplen * dx;
s += steplen * ds;
y(bound_idx) = s;
w += steplen * dw;
if(verbose){
cout <<"\tMean complementarity: " << mean_comp
<<"\n\tStep length: " << steplen
<<"\n\tCentering sigma: " << sigma << endl;
}
}
if(verbose){
cout << "Finished"
<<"\n\t Final mean complementarity: " << mean_comp << endl;
}
return SolverResult(x,y,iter);
}
// Start the optimization
SolverResult SolverGurobi::runOptimizer()
{
if (!getInitialized())
initialize();
try
{
// Create Gurobi environment and set parameters
GRBEnv env = GRBEnv();
env.set(GRB_IntParam_OutputFlag, 0);
GRBModel model = GRBModel(env);
// Get problem info
int numVars = constraints->getNumVariables();
int numConstraints = constraints->getNumConstraints();
// Get variables
auto variables = constraints->getVariables();
// Create array of model variables
GRBVar vars[numVars];
for (int i = 0; i < numVars; i++)
{
//vars[i] = model.addVar(0.0, 1.0, 0.0, GRB_BINARY);
// Set variable type
char type = GRB_CONTINUOUS;
if (variables.at(i)->getType() == VariableType::BINARY)
{
type = GRB_BINARY;
}
else if (variables.at(i)->getType() == VariableType::INTEGER)
{
type = GRB_INTEGER;
}
vars[i] = model.addVar(variables.at(i)->getLowerBound(),
variables.at(i)->getUpperBound(),
variables.at(i)->getCost(),
type);
}
// Integrate variables into model
model.update();
// Set starting points (does not help much...)
for (int i = 0; i < numVars; i++)
vars[i].set(GRB_DoubleAttr_Start, variables.at(i)->getValue());
/*
* Add constraints Ax <= b (or Ax = b)
* by evaluating gradient and build A matrix
*/
DenseVector x = DenseVector::Zero(numVars);
DenseVector dx = constraints->evalJacobian(x);
// Get constraint bounds
std::vector<double> clb;
std::vector<double> cub;
constraints->getConstraintBounds(clb,cub);
std::vector<int> rowGradient, colGradient;
constraints->structureJacobian(rowGradient, colGradient);
int nnzJacobian = constraints->getNumNonZerosJacobian();
// Add constraints one row at the time
for (int row = 0; row < numConstraints; row++)
{
// Build constraint
GRBLinExpr expr = 0;
// Loop through all non-zeros (inefficient)
for (int i = 0; i < nnzJacobian; i++)
{
if (rowGradient.at(i) == row)
{
int j = colGradient.at(i);
expr += dx(i)*vars[j];
}
}
// Add constraint to model
if (clb.at(row) == cub.at(row))
{
model.addConstr(expr, GRB_EQUAL, cub.at(row));
}
else
{
model.addConstr(expr, GRB_LESS_EQUAL, cub.at(row));
}
}
// More efficient method - avoids dense matrix
// std::vector<int> rows = {1,1,1,2,2,3,4,4,4,4,4,5};
// std::vector<int>::iterator start,stop;
// start = rows.begin();
// stop = start;
// while (start != rows.end())
// {
// while (stop != rows.end())
// {
// if (*stop == *start)
// ++stop;
// else
// break;
// }
// for (std::vector<int>::iterator it = start; it != stop; ++it)
// cout << *it << endl;
// start = stop;
// }
model.update();
assert(numVars == model.get(GRB_IntAttr_NumVars));
assert(numConstraints == model.get(GRB_IntAttr_NumConstrs));
// Optimize model
model.optimize();
// Check status
int optimstatus = model.get(GRB_IntAttr_Status);
if (optimstatus == GRB_INF_OR_UNBD)
{
model.getEnv().set(GRB_IntParam_Presolve, 0);
model.optimize();
optimstatus = model.get(GRB_IntAttr_Status);
}
// Create result object
SolverResult result(SolverStatus::ERROR, INF, std::vector<double>(numVars,0));
// Check Gurobi status
if (optimstatus == GRB_OPTIMAL)
{
result.status = SolverStatus::OPTIMAL;
// Get solution info
result.objectiveValue = model.get(GRB_DoubleAttr_ObjVal);
std::vector<double> optimalSolution;
for (int i = 0; i < numVars; i++)
{
optimalSolution.push_back(vars[i].get(GRB_DoubleAttr_X));
}
result.primalVariables = optimalSolution;
/*
* Reduced costs and constraint duals are
* only available for continuous models
*/
std::vector<double> reducedCosts;
std::vector<double> constraintDuals;
if (!model.get(GRB_IntAttr_IsMIP))
{
for (int i = 0; i < numVars; i++)
{
// Get reduced costs (related to range constraint duals)
reducedCosts.push_back(vars[i].get(GRB_DoubleAttr_RC));
}
for (int i = 0; i < numConstraints; i++)
{
GRBConstr c = model.getConstr(i);
double pi = c.get(GRB_DoubleAttr_Pi);
constraintDuals.push_back(pi);
}
}
result.lowerBoundDualVariables = reducedCosts;
result.upperBoundDualVariables = reducedCosts;
result.constraintDualVariables = constraintDuals;
return result;
}
else if (optimstatus == GRB_INFEASIBLE)
{
result.status = SolverStatus::INFEASIBLE;
result.objectiveValue = INF;
// compute and write out IIS
// model.computeIIS();
// model.write("problem.lp");
return result;
}
else if (optimstatus == GRB_UNBOUNDED)
{
result.status = SolverStatus::UNBOUNDED;
result.objectiveValue = -INF;
return result;
}
else
{
result.status = SolverStatus::ERROR;
result.objectiveValue = INF;
return result;
}
}
catch(GRBException e)
{
cout << "SolverGurobi: Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
return SolverResult(SolverStatus::ERROR, INF, std::vector<double>(constraints->getNumVariables(),0));
}
catch (...)
{
cout << "SolverGurobi: Error during optimization!" << endl;
return SolverResult(SolverStatus::ERROR, INF, std::vector<double>(constraints->getNumVariables(),0));
}
}
