1 | function model = mpt_solvenode(Matrices,lower,upper,OriginalModel,model,options) |
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2 | % This is the core code. Lot of pre-processing to get rid of strange stuff |
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3 | % arising from odd problems, big-M etc etc |
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4 | |
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5 | Matrices.lb = lower; |
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6 | Matrices.ub = upper; |
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7 | |
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8 | % Remove equality constraints and trivial stuff from big-M |
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9 | [equalities,redundant] = mpt_detect_fixed_rows(Matrices); |
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10 | Matrices = mpt_collect_equalities(Matrices,equalities); |
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11 | go_on_reducing = size(Matrices.Aeq,1)>0; |
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12 | Matrices = mpt_remove_equalities(Matrices,redundant); |
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13 | [Matrices,infeasible] = mpt_project_on_equality(Matrices); |
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14 | |
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15 | % We are not interested in explicit solutions over numerically empty regions |
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16 | parametric_empty = any(abs(Matrices.lb(end-Matrices.nx+1:end)-Matrices.ub(end-Matrices.nx+1:end)) < 1e-6); |
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17 | |
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18 | % Were the equality constraints found to be infeasible? |
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19 | if infeasible | parametric_empty |
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20 | return |
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21 | end |
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22 | |
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23 | % For some models with a lot of big-M stuff etc, the amount of implicit |
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24 | % equalities are typically large, making the LP solvers unstable if they |
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25 | % are not removed. To avoid problems, we iteratively detect fixed variables |
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26 | % and strenghten the bounds. |
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27 | fixed = find(Matrices.lb == Matrices.ub); |
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28 | infeasible = 0; |
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29 | while 0%~infeasible & options.mp.presolve |
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30 | [Matrices,infeasible] = mpt_derive_bounds(Matrices,options); |
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31 | if isequal(find(Matrices.lb == Matrices.ub),fixed) |
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32 | break |
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33 | end |
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34 | fixed = find(Matrices.lb == Matrices.ub); |
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35 | end |
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36 | |
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37 | % We are not interested in explicit solutions over numerically empty regions |
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38 | parametric_empty = any(abs(Matrices.lb(end-Matrices.nx+1:end)-Matrices.ub(end-Matrices.nx+1:end)) < 1e-6); |
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39 | |
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40 | if ~infeasible & ~parametric_empty |
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41 | |
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42 | while go_on_reducing & ~infeasible & options.mp.presolve |
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43 | [equalities,redundant] = mpt_detect_fixed_rows(Matrices); |
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44 | Matrices = mpt_collect_equalities(Matrices,equalities); |
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45 | go_on_reducing = size(Matrices.Aeq,1)>0; |
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46 | Matrices = mpt_remove_equalities(Matrices,redundant); |
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47 | [Matrices,infeasible] = mpt_project_on_equality(Matrices); |
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48 | M = Matrices; |
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49 | if go_on_reducing & ~infeasible |
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50 | [Matrices,infeasible] = mpt_derive_bounds(Matrices,options); |
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51 | end |
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52 | if infeasible |
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53 | % Numerical problems most likely because this infeasibility |
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54 | % should have been caught above. We have only cleaned the model |
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55 | Matrices = M; |
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56 | end |
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57 | end |
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58 | |
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59 | if ~infeasible |
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60 | if Matrices.qp |
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61 | if isequal(options.solver,'mplcp') |
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62 | [Pn,Fi,Gi,ac,Pfinal,details] = mpt_mpqp_mplcp(Matrices,options); |
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63 | else |
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64 | e = eig(full(Matrices.H)); |
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65 | if min(e) == 0 |
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66 | disp('Lack of strict convexity may lead to troubles in the mpQP solver') |
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67 | elseif min(e) < -1e-8 |
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68 | disp('Problem is not positive semidefinite! Your mpQP solution may be completely wrong') |
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69 | elseif min(e) < 1e-5 |
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70 | disp('QP is close to being (negative) semidefinite, may lead to troubles in mpQP solver') |
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71 | end |
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72 | %Matrices.H = Matrices.H + eye(length(Matrices.H))*1e-4; |
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73 | [Pn,Fi,Gi,ac,Pfinal,details] = mpt_mpqp(Matrices,options.mpt); |
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74 | end |
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75 | else |
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76 | if isequal(options.solver,'mplcp') |
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77 | [Pn,Fi,Gi,ac,Pfinal,details] = mpt_mpqp_mplcp(Matrices,options); |
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78 | else |
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79 | [Pn,Fi,Gi,ac,Pfinal,details] = mpt_mplp(Matrices,options.mpt); |
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80 | end |
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81 | end |
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82 | [Fi,Gi,details] = mpt_project_back_equality(Matrices,Fi,Gi,details,OriginalModel); |
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83 | [Fi,Gi] = mpt_select_rows(Fi,Gi,Matrices.requested_variables); |
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84 | [Fi,Gi] = mpt_clean_optmizer(Fi,Gi); |
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85 | model = mpt_appendmodel(model,Pfinal,Pn,Fi,Gi,details); |
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86 | end |
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87 | else |
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88 | |
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89 | end |
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90 | |
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91 | function [Pn,Fi,Gi,ac,Pfinal,details] = mpt_mpqp_mplcp(Matrices,options) |
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92 | |
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93 | if Matrices.qp |
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94 | lcpData = lcp_mpqp(Matrices); |
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95 | BB = mplcp(lcpData) |
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96 | [Pn,Fi,Gi] = soln_to_mpt(lcpData,BB); |
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97 | else |
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98 | lcpData = lcp_mplp(Matrices); |
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99 | BB = mplcp(lcpData) |
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100 | [Pn,Fi,Gi] = soln_to_mpt(lcpData,BB); |
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101 | end |
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102 | Pfinal = union(Pn); |
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103 | if Matrices.qp |
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104 | for i=1:length(Fi) |
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105 | details.Ai{i} = 0.5*Fi{i}'*Matrices.H*Fi{i} + 0.5*(Matrices.F*Fi{i}+Fi{i}'*Matrices.F') + Matrices.Y; |
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106 | details.Bi{i} = Matrices.Cf*Fi{i}+Gi{i}'*Matrices.F' + Gi{i}'*Matrices.H*Fi{i} + Matrices.Cx; |
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107 | details.Ci{i} = Matrices.Cf*Gi{i}+0.5*Gi{i}'*Matrices.H*Gi{i} + Matrices.Cc; |
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108 | end |
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109 | else |
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110 | for i=1:length(Fi) |
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111 | details.Ai{i} = []; |
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112 | details.Bi{i} = Matrices.H*Fi{i}; |
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113 | details.Ci{i} = Matrices.H*Gi{i}; |
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114 | end |
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115 | end |
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116 | ac = []; |
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