非線形最適化ライブラリNloptの概要

非線形最適化ライブラリNlopt
Nloptは軽量レベルのオープンソース非線形最適化ライブラリであり,多様な最適化アルゴリズムに統一されたインタフェースを提供する.ホームページ:https://nlopt.readthedocs.io/en/latest/ git:https://github.com/stevengj/nlopt
目次

非線形最適化ライブラリNlopt

目次

ダウンロードインストール

API

nlopt_create

nlopt_set_min_objective

nlopt_set_lower_bounds

nlopt_add_inequality_constraint

nlopt_set_stopval

nlopt_minimize_econstrained

return value

ダウンロード
ダウンロード:nlopt-2.4.2.tar.gzインストール:

./configure && make && sudo make install

API
nlopt_create nlopt_createは、与えられた最適化アルゴリズムnlopt_algorithmに従ってnlopt_optオブジェクトを返し、nは最適化変数次元数である

nlopt_opt nlopt_create(nlopt_algorithm algorithm, unsigned n);

nlopt_algorithm含む

typedef enum {
     /* Naming conventions:

        NLOPT_{G/L}{D/N}_* 
        = global/local derivative/no-derivative optimization, 
              respectively 

    *_RAND algorithms involve some randomization.

    *_NOSCAL algorithms are *not* scaled to a unit hypercube
             (i.e. they are sensitive to the units of x)
    */

     NLOPT_GN_DIRECT = 0,
     NLOPT_GN_DIRECT_L,
     NLOPT_GN_DIRECT_L_RAND,
     NLOPT_GN_DIRECT_NOSCAL,
     NLOPT_GN_DIRECT_L_NOSCAL,
     NLOPT_GN_DIRECT_L_RAND_NOSCAL,

     NLOPT_GN_ORIG_DIRECT,
     NLOPT_GN_ORIG_DIRECT_L,

     NLOPT_GD_STOGO,
     NLOPT_GD_STOGO_RAND,

     NLOPT_LD_LBFGS_NOCEDAL,

     NLOPT_LD_LBFGS,

     NLOPT_LN_PRAXIS,

     NLOPT_LD_VAR1,
     NLOPT_LD_VAR2,

     NLOPT_LD_TNEWTON,
     NLOPT_LD_TNEWTON_RESTART,
     NLOPT_LD_TNEWTON_PRECOND,
     NLOPT_LD_TNEWTON_PRECOND_RESTART,

     NLOPT_GN_CRS2_LM,

     NLOPT_GN_MLSL,
     NLOPT_GD_MLSL,
     NLOPT_GN_MLSL_LDS,
     NLOPT_GD_MLSL_LDS,

     NLOPT_LD_MMA,

     NLOPT_LN_COBYLA,

     NLOPT_LN_NEWUOA,
     NLOPT_LN_NEWUOA_BOUND,

     NLOPT_LN_NELDERMEAD,
     NLOPT_LN_SBPLX,

     NLOPT_LN_AUGLAG,
     NLOPT_LD_AUGLAG,
     NLOPT_LN_AUGLAG_EQ,
     NLOPT_LD_AUGLAG_EQ,

     NLOPT_LN_BOBYQA,

     NLOPT_GN_ISRES,

     /* new variants that require local_optimizer to be set,
    not with older constants for backwards compatibility */
     NLOPT_AUGLAG,
     NLOPT_AUGLAG_EQ,
     NLOPT_G_MLSL,
     NLOPT_G_MLSL_LDS,

     NLOPT_LD_SLSQP,

     NLOPT_LD_CCSAQ,

     NLOPT_GN_ESCH,

     NLOPT_NUM_ALGORITHMS /* not an algorithm, just the number of them */
} nlopt_algorithm;

アルゴリズムの詳細:https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/
nlopt_set_min_objective nlopt_set_min_objectiveとnlopt_set_max_objectiveはnlopt_opt設定目標関数nlopt_func

nlopt_result nlopt_set_min_objective(nlopt_opt opt, nlopt_func f, void* f_data);
nlopt_result nlopt_set_max_objective(nlopt_opt opt, nlopt_func f, void* f_data);

nlopt_funcの定義は、nが次元数、xが入力、gradが勾配戻り値、f_dataが関数に必要な入力のカスタムパラメータです.

 double f(unsigned n, const double* x, double* grad, void* f_data);

nlopt_set_lower_bounds nlopt_set_lower_boundsとnlopt_set_upper_bounds最適化変数上下境界を設定

nlopt_result nlopt_set_lower_bounds(nlopt_opt opt, const double* lb);
nlopt_result nlopt_set_upper_bounds(nlopt_opt opt, const double* ub);

nlopt_add_inequality_constraint nlopt_add_inequality_constraintとnlopt_add_equality_constraintはnlopt_optに不等式と等式の制約を追加

nlopt_result nlopt_add_inequality_constraint(nlopt_opt opt, nlopt_func fc, void* fc_data, double tol);
nlopt_result nlopt_add_equality_constraint(nlopt_opt opt, nlopt_func h, void* h_data, double tol);

nlopt_set_stopval nlopt_set_stopvalnlopt_set_ftol_relnlopt_set_ftol_absnlopt_set_xtol_relnlopt_set_xtol_absはnlopt_optに停止条件を設定

nlopt_result nlopt_set_stopval(nlopt_opt opt, double stopval);
nlopt_result nlopt_set_ftol_rel(nlopt_opt opt, double tol);
nlopt_result nlopt_set_ftol_abs(nlopt_opt opt, double tol);
nlopt_result nlopt_set_xtol_rel(nlopt_opt opt, double tol);
nlopt_result nlopt_set_xtol_abs(nlopt_opt opt, const double* tol);

nlopt_minimize_econstrained nlopt_minimize_econstrainedを直接呼び出して最適化計算を完了できます.

nlopt_result
NLOPT_STDCALL nlopt_minimize_econstrained(
     nlopt_algorithm algorithm,
     int n, nlopt_func_old f, void *f_data,
     int m, nlopt_func_old fc, void *fc_data_, ptrdiff_t fc_datum_size,
     int p, nlopt_func_old h, void *h_data_, ptrdiff_t h_datum_size,
     const double *lb, const double *ub, /* bounds */
     double *x, /* in: initial guess, out: minimizer */
     double *minf, /* out: minimum */
     double minf_max, double ftol_rel, double ftol_abs,
     double xtol_rel, const double *xtol_abs,
     double htol_rel, double htol_abs,
     int maxeval, double maxtime)

return value

/*Successful termination (positive return values)*/
NLOPT_SUCCESS` `=` `1
/*Generic success return value.*/

NLOPT_STOPVAL_REACHED` `=` `2
/*Optimization stopped because stopval (above) was reached.*/

NLOPT_FTOL_REACHED` `=` `3
/*Optimization stopped because ftol_rel or ftol_abs (above) was reached.*/

NLOPT_XTOL_REACHED` `=` `4
/*Optimization stopped because xtol_rel or xtol_abs (above) was reached.*/

NLOPT_MAXEVAL_REACHED` `=` `5
/*Optimization stopped because maxeval (above) was reached.*/

NLOPT_MAXTIME_REACHED` `=` `6
/*Optimization stopped because maxtime (above) was reached.*/

/*Error codes (negative return values)*/
NLOPT_FAILURE` `=` `-1
/*Generic failure code.*/

NLOPT_INVALID_ARGS` `=` `-2
/*Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera).*/

NLOPT_OUT_OF_MEMORY` `=` `-3
/*Ran out of memory.*/

NLOPT_ROUNDOFF_LIMITED` `=` `-4
/*Halted because roundoff errors limited progress. (In this case, the optimization still typically returns a useful result.)*/

NLOPT_FORCED_STOP` `=` `-5
/*Halted because of a forced termination: the user called nlopt_force_stop(opt) on the optimization’s  nlopt_opt object opt from the user’s objective function or constraints.*/