1. Volume and Surface Area of Star Convex Set
2. Volume and Surface Area of Piecewise Linear Convex Set
3. Volume and Surface Area of Quadratically Constrained Star Set
4. Volume and Surface Area of Nonlinear Constrained Star Set
5. Direction Search Method for Solving Star Convex Optimization
6. Direction Search Method for Solving Linear Programming
7. Direction Search Method for Solving Quadratic Programming
8. Direction Search Method for Solving Nonlinear Programming
9. Direction Search Method v.s. Interior Point Method
ÐìË®Á¼Ò»¶¨»áÈ϶¨ÎÒ²»¶®Í³¼ÆÑ§£¬¾ÓȻҪÏòͳ¼ÆÑ§ÆÚ¿¯Í¶¸åÂÛÎÄ¡£Ò²²»ÖªµÀÐìË®Á¼ÈçºÎ¾ÍÖªµÀÎÒÒªÏòͳ¼ÆÑ§ÆÚ¿¯Í¶¸åÂÛÎÄ¡£
Èç¹ûÐìË®Á¼»ØÀ´£¬Ò»¶¨ÓÖ»áÈ¥ÉÏÍø²éÔÄ£¬Ëæºó¾Í»á˵ÎÒͶ¸åµÄÆÚ¿¯¶¼ÊÇÃÀ¹ú´óѧµÄУ¿¯£¬ÊÇûÈËÀí»áµÄQ1Ä©Á÷ÆÚ¿¯¡£
ÕâÀïµÄºÜ¶àÈËÈ϶¨ÉÏÊöÎÊÌâ¶¼ÊÇÊ®·Ö¼òµ¥µÄÎÊÌâ¡£Èç¹ûÉÏÍøËÑË÷£¬¾Í»á·¢ÏÖ½ØÖÁĿǰ£¬»¹ÓкܶàÂÛÎÄÊǹØÓÚn-Dimensional Ellipsoid µÄÂÛÎÄ¡£¶øEllipsoidÎÊÌâÊÇÒ»ÖÖ×î×î¼òµ¥µÄStar Convex¡£Ä¿Ç°»¹Ã»ÓÐʲôÂÛÎÄÊǹØÓÚ¼ÆËãÒ»°ãÍâ͹¶àÃæÌåµÄÌå»ýºÍÃæ»ýµÄÂÛÎÄ¡£
ÐìË®Á¼Ò»Ìý˵ÏßÐÔ£¬¾ÍÒ»¶¨ÈÏΪӦ¸ÃÓ÷ÇÏßÐÔ»òÕßÓÃÕý̬·Ö²¼À´½â¾ö¡£¿ÉËû²»ÖªµÀµÄÊÇ£¬ÏÖ´úÊýѧµÄÁ½¸ö×îÖØÒªµÄËã·¨ÊÇInterior Point MethodºÍSimplex Method£¬¶¼ÊÇÊ×ÏÈ×ÅÑÛÓÚÏßÐԹ滮µÄËã·¨¡£
2. Volume and Surface Area of Piecewise Linear Convex Set
3. Volume and Surface Area of Quadratically Constrained Star Set
4. Volume and Surface Area of Nonlinear Constrained Star Set
5. Direction Search Method for Solving Star Convex Optimization
6. Direction Search Method for Solving Linear Programming
7. Direction Search Method for Solving Quadratic Programming
8. Direction Search Method for Solving Nonlinear Programming
9. Direction Search Method v.s. Interior Point Method
ÐìË®Á¼Ò»¶¨»áÈ϶¨ÎÒ²»¶®Í³¼ÆÑ§£¬¾ÓȻҪÏòͳ¼ÆÑ§ÆÚ¿¯Í¶¸åÂÛÎÄ¡£Ò²²»ÖªµÀÐìË®Á¼ÈçºÎ¾ÍÖªµÀÎÒÒªÏòͳ¼ÆÑ§ÆÚ¿¯Í¶¸åÂÛÎÄ¡£
Èç¹ûÐìË®Á¼»ØÀ´£¬Ò»¶¨ÓÖ»áÈ¥ÉÏÍø²éÔÄ£¬Ëæºó¾Í»á˵ÎÒͶ¸åµÄÆÚ¿¯¶¼ÊÇÃÀ¹ú´óѧµÄУ¿¯£¬ÊÇûÈËÀí»áµÄQ1Ä©Á÷ÆÚ¿¯¡£
ÕâÀïµÄºÜ¶àÈËÈ϶¨ÉÏÊöÎÊÌâ¶¼ÊÇÊ®·Ö¼òµ¥µÄÎÊÌâ¡£Èç¹ûÉÏÍøËÑË÷£¬¾Í»á·¢ÏÖ½ØÖÁĿǰ£¬»¹ÓкܶàÂÛÎÄÊǹØÓÚn-Dimensional Ellipsoid µÄÂÛÎÄ¡£¶øEllipsoidÎÊÌâÊÇÒ»ÖÖ×î×î¼òµ¥µÄStar Convex¡£Ä¿Ç°»¹Ã»ÓÐʲôÂÛÎÄÊǹØÓÚ¼ÆËãÒ»°ãÍâ͹¶àÃæÌåµÄÌå»ýºÍÃæ»ýµÄÂÛÎÄ¡£
ÐìË®Á¼Ò»Ìý˵ÏßÐÔ£¬¾ÍÒ»¶¨ÈÏΪӦ¸ÃÓ÷ÇÏßÐÔ»òÕßÓÃÕý̬·Ö²¼À´½â¾ö¡£¿ÉËû²»ÖªµÀµÄÊÇ£¬ÏÖ´úÊýѧµÄÁ½¸ö×îÖØÒªµÄËã·¨ÊÇInterior Point MethodºÍSimplex Method£¬¶¼ÊÇÊ×ÏÈ×ÅÑÛÓÚÏßÐԹ滮µÄËã·¨¡£
���à¼Ê±ï¿½ï¿½: 2023-05-07 04:36:07



