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Optimization Theory
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1. ÀÏ º¯¼ö ÇÔ¼öÀÇ ÃÖ´ëÃÖ¼Ò ÀÌ·Ð
1.1 ÀÏ º¯¼ö ÇÔ¼ö ¹ÌºÐ
1.2 Å×ÀÏ·¯ ±Þ¼ö(Taylor Series)
1.3 Taylor ±Þ¼ö º¸Ãæ¼³¸í[Áõ¸í]
2. ´Ùº¯¼ö ÇÔ¼ö
2.1 ´Ùº¯¼ö ÇÔ¼ö(Multi Variable Functions)ÀÇ Á¤ÀÇ:
2.2 ´Ùº¯¼ö ÇÔ¼öÀÇ ¹ÌºÐ
2.3 f: R^n -¡µ R ÀÇ Å×ÀÏ·¯ ±Þ¼ö(Taylor Series)
2.4 f: R^m -¡µ R^n ÀÇ Å×ÀÏ·¯ ±Þ¼ö(Taylor Series)
2.5 ·¹º§ÁýÇÕ°ú ±×·¹µð¾ðÆ® ¹æÇâ
3. ÄÁº¤½º ÇÔ¼ö(Convex function)
3.1 ÄÁº¤½º ÇÔ¼öÀÇ Á¤ÀÇ
3.1-11 Á¤¸®(ÄÁº¤½º ÇÔ¼ö ÇÙ½ÉÁ¤¸®)
4. Á¦¾à Á¶°ÇÀÌ ¾ø´Â ÃÖÀûÈ
4.1 ±âº»°³³ä
4.2-1 ÇÏ°¹æÇâ ã±â 1[Gradient Descent Ž»ö¹æ¹ý]
4.2-2 Á÷¼±Å½»ö(Line search) ¾Ë°í¸®Áò: º¸Æø(step size)°áÁ¤Çϱâ
4.3 ÇÏ°¹æÇâ ã±â 2[Conjugate Gradient Ž»ö¹æ¹ý]
4.4 ÇÏ°¹æÇâ ã±â 3 [Newton Ž»ö¹æ¹ý]
4.4-1 Newton Ž»ö¹æ¹ý
4.4-2 Levenberg-Marquardt Type Damped Newton Method
4.4-3: Quasi-Newton Method
4.5 ºñ¼±Çü ÃÖ¼ÒÀڽ¹ý(non-linear least squares problem)
4.5-1: ´Ùº¯¼ö ÇÔ¼öÀÇ ±¹¼Ò ¼±Çü¼ºÁú
4.5-2: ºñ¼±Çü ÃÖ¼ÒÀڽ¹ý(non-linear least squares problem)
4.5-3: Gauss-Newton Ž»ö¹æ¹ý
4.5-4: Levenberg-Marquardt ¹æ¹ý
5. ¶ó±×¶ûÁÖ ½Â¼ö¹ý(Lagrange multiplier method)
5.1 ¶ó±×¶ûÁÖ ½Â¼ö¹ý(Lagrange multiplier method)
-µîÈ£ Á¦¾àÁ¶°ÇÀÌ ÀÖ´Â °æ¿ì5.2 ¶ó±×¶ûÁÖ ½Â¼ö¹ý(Lagrange multiplier method)
-µîÈ£¿Í ºÎµîÈ£ Á¦¾àÁ¶°ÇÀÌ ÀÖ´Â °æ¿ì6. ¼±Çü´ë¼öÇÐ
6.1 º¤ÅÍ°ø°£ R^n (Vector space of R^n)
6.2 ºÎºÐ°ø°£(Subspace): º¤ÅÍ°ø°£¼ÓÀÇ º¤ÅÍ°ø°£
6.3 ÀÏÂ÷°áÇÕ(linear combination)ÀÇ ±âÇÏÇÐÀûÀÎ ÀǹÌ: ÆòÇà»çº¯Çü ¹ýÄ¢
6.4 ÀÏÂ÷µ¶¸³, ÀÏÂ÷Á¾¼Ó
6.5 ±âÀú°³³ä(Basis)°ú º¤ÅÍ°ø°£ÀÇ Â÷¿ø(Dimension)
6.6 ³» Àû (Inner product)
6.7 Çà ·Ä (Matrices)
6.8 º¤ÅÍ°ø°£°ú Çà·Ä°úÀÇ °ü°è
6.9 Çà·Ä¿¡¼ ¿º¤ÅÍ¿Í Ç຤ÅÍÀÇ ÀǹÌ
6.10 °íÀ¯Ä¡¿Í °íÀ¯º¤ÅÍÀÇ ±âÇÏÇÐÀûÀÎ ÀǹÌ
6.11 ¾ç È®Á¤Çà·Ä¿¡ ´ëÇÑ Gram-Schmidt(±×¶÷-½´¹ÌÆ®) Á÷±³È °úÁ¤
6.12 ±º·ÐÀÇ Á¤ÀÇ(Definition of Group)
6.13 R^3¿¡¼ÀÇ Á÷±³Çà·Ä(Orthogonal Matrix in R^3)
6.14 °ø°£»óÀÇ ¹°Ã¼ÀÇ È¸Àü°ú ±º ÀÌ·Ð: SO_3(R)
6.15 ¼±Çü¹æÁ¤½ÄÀÇ Çر¸Çϱâ: Ax=b
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