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ä»åã¯ä¹ ãã¶ãã«Rã®è©±é¡ã 2次è¨ç»åé¡ã解ãã®ã«ãRã®"quadprog"ããã±ã¼ã¸ã使ããã¨ã«ããã ä¾é¡ã¯æ±å·¥å¤§ã®æ°´éå çã®ãµã¤ãâ http://www.me.titech.ac.jp/~mizu_lab/text/pdf-file/LP9-QP-problem.pdf ä¾é¡ã§ã¯å¶ç´ãçå¼å¶ç´ã§ãããã ãquadprogã§æ±ããå¶ç´ã¯ä¸çå¼å¶ç´ã§ããã çå¼å¶ç´ãä¸çå¼å¶ç´ã«å¤ããã®ã¯é£ãããªãã ãªãã°ã ã¨ãã2ã¤ã®å¶ç´ã«è½ã¨ãè¾¼ãã°ããã # TODO: ç義2次è¨ç»åé¡ã解ã ############################################################################### setwd("H:\\RW\\QPTest") library(quadprog) ## ## Assume we want to minim
RjpWiki ã¯ãªã¼ãã³ã½ã¼ã¹ã®çµ±è¨è§£æã·ã¹ãã R ã«é¢ããæ å ±äº¤æãç®çã¨ãã Wiki ã§ãç·å½¢ä¸çå¼å¶ç´ä»ãã®æé©åé¢æ° constrOptim() constrOptim é¢æ°ã¯ adaptive barrier ã¢ã«ã´ãªãºã (å¶ç´é åã®å¢çã«è¿ä»ãã¨ç®çé¢æ°å¤ãå¢å ãããããªä»å é ãé©å®ä»ãå ãã?)ãç¨ããç·å½¢ä¸çå¼å¶ç´(ã¤ã¾ãç¡éãããã¯æçãªå¤è§å½¢å ã§ã®æå°å¤æ±ãã)ä¸ã§é¢æ°ãæå°åãããå é¨çã« optim() é¢æ°ã使ããç©å½¢å¶ç´ä»ãã®æé©å㯠otpim ã® method="L-BGFS-B" ã使ããã æ¸å¼ (method ãªãã·ã§ã³ã®æ¢å®å¤ã®ä¸ãæ¹ã«ã³ã£ããï¼) constrOptim(theta, f, grad, ui, ci, mu = 1e-04, control = list(), method = if(is.null(grad)) "Neld
ã¢ã«ã´ãªãºã ã¨ã¯æ¥æ¬èªã§ã¯å¦çæé ã®ãã¨ãè¨ãã¾ãã æ±ç¨æ°çè¨ç»æ³ããã±ã¼ã¸ Nuorium Optimizer ãè²ã ãªåé¡ã解ããã¨ãã§ããã®ã¯æ§ã ãªã¢ã«ã´ãªãºã ãããã°ã©ã ããã¦ããããã§ãã ããã§ã¯æ°çè¨ç»æ³ã»æé©åã®ä»çµã¿ãç解ããä¸ã§å¿ è¦ãªæ å ±ãåãããããã説æè´ãã¾ãã ããã¾ã§å ¥éçãªä½ç½®ã¥ãã§ãã®ã§æ°å¦çã«å³å¯ãªèª¬æãè¡ã訳ã§ã¯ãããã¾ããã®ã§ãäºæ¿ãã ããã æ°çè¨ç»æ³ã§ä»£è¡¨çãªã¢ã«ã´ãªãºã ã«ã¤ãã¦ã®ç°¡åãªè§£èª¬ ç·å½¢è¨ç»æ³ï¼LPï¼ æ··åæ´æ°ç·å½¢è¨ç»æ³ï¼MILPï¼ æ´æ°è¨ç»æ³ï¼IPï¼ å¸äºæ¬¡è¨ç»æ³ï¼CQPï¼ éç·å½¢è¨ç»æ³ï¼NLPï¼ ã¢ã«ã´ãªãºã ã®èª¬æ ã¢ã«ã´ãªãºã ã®èª¬æãå ·ä½ä¾ãè¦ãªããè¡ãããã¨æãã¾ãã ä¾é¡ 8 æã®é貨ãè¢ã«å ¥ããé貨ã»ããã 1000 è¢è²©å£²ãã¾ãã è¢ã« 8 æã®é貨ãå ¥ããä½æ¥ãããæ¥è ã«ä¾é ¼ããã®ã§ããã ãã®æ¥è 㯠1 è¢ããã 1
å¸äºæ¬¡è¨ç» (convex quadratic programming)â 次ã®å¸äºæ¬¡è¨ç»åé¡ã®è§£æ³ã®ãã¨ï¼ å¸äºæ¬¡è¨ç»åé¡ ç®çé¢æ°ï¼\(\min\; \frac{1}{2}\mathbf{x}^\top Q\mathbf{x}+\mathbf{c}^\top\mathbf{x}\) å¶ç´æ¡ä»¶ï¼\(A\mathbf{x}=\mathbf{b}\)ï¼\(C\mathbf{x}\ge \mathbf{d}\) ãã ãï¼å ¥åãã¯ãã« \(\mathbf{x}=[x_1,x_2,\ldots,x_N]^\top\)ï¼\(Q\) 㯠NÃN ã®æ£å®å¤è¡åï¼\(A\) 㨠\(C\) ã¯MÃNè¡åï¼\(\mathbf{c}\) ã¯N次ã®ãã¯ãã«ï¼\(\mathbf{d}\) 㨠\(\mathbf{b}\) ã¯M次ã®ãã¯ãã«ï¼ ä¸è¬ã®éç·å½¢æé©ååé¡ã§ã¯å¤§åæé©è§£ãæ±ããã®ãé£ããï¼ ãããï¼ãã®å¸
Description Minimise a function subject to linear inequality constraints using an adaptive barrier algorithm. Usage constrOptim(theta, f, grad, ui, ci, mu = 1e-04, control = list(), method = if(is.null(grad)) "Nelder-Mead" else "BFGS", outer.iterations = 100, outer.eps = 1e-05, ..., hessian = FALSE) Arguments
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