This paper provides a gradient search algorithm for finding the maximal visible area polygon (VAP) viewed by an interior point in a simple polygon P. The algorithm is based on a natural partition of P into convex sets...This paper provides a gradient search algorithm for finding the maximal visible area polygon (VAP) viewed by an interior point in a simple polygon P. The algorithm is based on a natural partition of P into convex sets, such that each element of the partition is associated with a unique analytical form of the area function. We call this partition a back diagonal partition of P. Our maximal VAP algorithm converges in a finite number of steps, and is polynomial with a complexity of , for a simple polygon P with n vertices, and r reflex vertices. We use the maximal VAP algorithm as a basis for a greedy heuristic for the well known guardhouse problem with a computation complexity of .展开更多
Motion estimation is an important part of the MPEG- 4 encoder, due to its significant impact on the bit rate and the output quality of the encoder sequence. Unfortunately this feature takes a significant part of the e...Motion estimation is an important part of the MPEG- 4 encoder, due to its significant impact on the bit rate and the output quality of the encoder sequence. Unfortunately this feature takes a significant part of the encoding time especially when the straightforward full search(FS) algorithm is used. In this paper, a new algorithm named diamond block based gradient descent search (DBBGDS) algorithm, which is significantly faster than FS and gives similar quality of the output sequence, is proposed. At the same time, some other algorithms, such as three step search (TSS), improved three step search (ITSS), new three step search (NTSS), four step search (4SS), cellular search (CS) , diamond search (DS) and block based gradient descent search (BBGDS), are adopted and compared with DBBGDS. As the experimental results show, DBBGDS has its own advantages. Although DS has been adopted by the MPEG- 4 VM, its output sequence quality is worse than that of the proposed algorithm while its complexity is similar to the proposed one. Compared with BBGDS, the proposed algorithm can achieve a better output quality.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under...In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.展开更多
In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmo...In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.展开更多
文摘This paper provides a gradient search algorithm for finding the maximal visible area polygon (VAP) viewed by an interior point in a simple polygon P. The algorithm is based on a natural partition of P into convex sets, such that each element of the partition is associated with a unique analytical form of the area function. We call this partition a back diagonal partition of P. Our maximal VAP algorithm converges in a finite number of steps, and is polynomial with a complexity of , for a simple polygon P with n vertices, and r reflex vertices. We use the maximal VAP algorithm as a basis for a greedy heuristic for the well known guardhouse problem with a computation complexity of .
文摘Motion estimation is an important part of the MPEG- 4 encoder, due to its significant impact on the bit rate and the output quality of the encoder sequence. Unfortunately this feature takes a significant part of the encoding time especially when the straightforward full search(FS) algorithm is used. In this paper, a new algorithm named diamond block based gradient descent search (DBBGDS) algorithm, which is significantly faster than FS and gives similar quality of the output sequence, is proposed. At the same time, some other algorithms, such as three step search (TSS), improved three step search (ITSS), new three step search (NTSS), four step search (4SS), cellular search (CS) , diamond search (DS) and block based gradient descent search (BBGDS), are adopted and compared with DBBGDS. As the experimental results show, DBBGDS has its own advantages. Although DS has been adopted by the MPEG- 4 VM, its output sequence quality is worse than that of the proposed algorithm while its complexity is similar to the proposed one. Compared with BBGDS, the proposed algorithm can achieve a better output quality.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.
文摘In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.
