In order to reduce the torque ripple,increase the average torque and optimize the drive performance of the switched reluctance motor (SRM),the nonlinear dynamic model of SRM is established in the MATLAB /Simulink envi...In order to reduce the torque ripple,increase the average torque and optimize the drive performance of the switched reluctance motor (SRM),the nonlinear dynamic model of SRM is established in the MATLAB /Simulink environment.The effects of the turn-on and turn-off angles are investigated by the simulation results of the dynamic model,and the function is made among the rotor speed,turn-on angle and turn-off angle.To optimize the torque dynamic performance,the two-objective simultaneous optimization function is proposed by two weight factors.And the optimized turn-on and turn-off angles as functions of rotor speed are developed by using the simultaneous optimization method.Then the optimized torque controller is designed based on the optimized turn-on and turn-off angles.The simulation results show that the optimized torque controller designed in this paper can effectively reduce the torque ripple and increase the average torque,and optimize the torque dynamic performance of the SRM.展开更多
A novel methodology is presented for simultaneously optimizing synthesis and cleaning schedule of flexible heat exchanger network(HEN)by genetic/simulated annealing algorithms(GA/SA).Through taking into account the ef...A novel methodology is presented for simultaneously optimizing synthesis and cleaning schedule of flexible heat exchanger network(HEN)by genetic/simulated annealing algorithms(GA/SA).Through taking into account the effect of fouling process on optimal network topology,a preliminary network structure possessing two-fold oversynthesis is obtained by means of pseudo-temperature enthalpy(T-H)diagram approach prior to simultaneous optimization.Thus,the computational complexity of this problem classified as NP(Non-deterministic Polynomial)-complete can be significantly reduced.The promising matches resulting from preliminary synthesis stage are further optimized in parallel with their heat exchange areas and cleaning schedule.In addition,a novel continu- ous time representation is introduced to subdivide the given time horizon into several variable-size intervals according to operating periods of heat exchangers,and then flexible HEN synthesis can be implemented in dynamic manner.A numerical example is provided to demonstrate that the presented strategy is feasible to decrease the total annual cost(TAC)and further improve network flexibility,but even more important,it may be applied to solve large-scale flexible HEN synthesis problems.展开更多
Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their d...Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their doses for the experiment are selected according to the characteristics of the zinc sulfate solution. Then, the reagent doses are optimized by analyzing the influence of reagent dose on the polarographic parameters(i.e. half-wave potential E_(1/2) and limiting diffusion current I_p). Finally, the optimization results are verified by simultaneously determining trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+). The determination results indicate that the optimized reagents exhibit wide linearity, low detection limits, high accuracy and good precision for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+).展开更多
A new prestack AVA simultaneous inversion using particle swarm optimization algorithm is proposed, which can obtain the elastic parameters such as P-wave and S-wave impedance from P-wave reflection data simultaneously...A new prestack AVA simultaneous inversion using particle swarm optimization algorithm is proposed, which can obtain the elastic parameters such as P-wave and S-wave impedance from P-wave reflection data simultaneously. Compared with the conventional AVA inversion based on generalized linear technique, this method does not depend on the initial model and can reach the global minimum. In order to increase the stability of the inversion, low-frequency trends of P-wave and S-wave impedances are built into the inversion. This method has been successfully applied to synthetic and field data. The estimated P-wave and S-wave impedances can be combined to derive other elastic parameters, which are sensitive for lithology identification and fluid prediction.展开更多
An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ab...An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at dement knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refine- ment more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting dements to track optimal control profile breakpoints and ensure accurate state and centrol profiles. Four classic benchmarks of dynamic op- timization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferz,ble in improving the solution accuracy of chemical dy- namic optimization problem.展开更多
Chinese rice wine making is a typical simultaneous saccharification and fermentation （SSF） process. During the fermentation process, temperature is one of the key parameters which decide the quality of Chinese rice ...Chinese rice wine making is a typical simultaneous saccharification and fermentation （SSF） process. During the fermentation process, temperature is one of the key parameters which decide the quality of Chinese rice wine. To optimize the SSF process for Chinese rice wine brewing, the effects of temperature on the kinetic parameters of yeast growth and ethanol production at various temperatures were determined in batch cultures using a mathematical model. The kinetic parameters as a function of temperature were evaluated using the software Origin8.0. Combing these functions with the mathematical model, an appropriate form of the model equations for the SSF considering the effects of temperature were developed. The kinetic parameters were found to fit the experimental data satisfactorily with the developed temperature-dependent model. The temperature profile for maximizing the ethanol production for rice wine fermentation was determined by genetic algorithm. The optimum temperature profile began at a low temperature of 26℃ up to 30 h. The operating temperature increased rapidly to 31.9 ℃, and then decreased slowly to 18℃ at 65 h. Thereafter, the temperature was maintained at 18 ℃ until the end of fermentation. A maximum ethanol production of 89.3 g.L 1 was attained. Conceivably, our model would facilitate the improvement of Chinese rice wine production at the industrial scale.展开更多
This article attempts to develop a simultaneous optimization procedure of several response variables from incomplete multi-response experiments. In incomplete multi-response experiments all the responses (p) are not r...This article attempts to develop a simultaneous optimization procedure of several response variables from incomplete multi-response experiments. In incomplete multi-response experiments all the responses (p) are not recorded from all the experimental units (n). Two situations of multi-response experiments considered are (i) on units all the responses are recorded while on units a subset of responses is recorded and (ii) on units all the responses (p) are recorded, on units a subset of responses is recorded and on units the remaining subset of responses is recorded. The procedure of estimation of parameters from linear multi-response models for incomplete multi-response experiments has been developed for both the situations. It has been shown that the parameter estimates are consistent and asymptotically unbiased. Using these parameter estimates, simultaneous optimization of incomplete multi-response experiments is attempted following the generalized distance criterion [1]. For the implementation of these procedures, SAS codes have been developed for both complete (k ≤ 5, p = 5) and incomplete (k ≤ 5, p1 = 2, 3 and p2 = 2, 3, where k is the number of factors) multi-response experiments. The procedure developed is illustrated with the help of a real data set.展开更多
An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are mad...An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.展开更多
The effects of process variables in Simultaneous Saccharification and Fermentation (SSF) of wheat bran flour were studied in bulk fermentation using a coculture of Aspergillus niger - Kluveromyces marxianus. The effec...The effects of process variables in Simultaneous Saccharification and Fermentation (SSF) of wheat bran flour were studied in bulk fermentation using a coculture of Aspergillus niger - Kluveromyces marxianus. The effect of substrate density, pH, temperature, and enzyme concentration on wheat bran was predicted by designing experiments in which a single parameter is varied keeping other variables at a constant level. The above parameters were optimized for a batch culture in a fermentor. Optimal values for substrate concentration, pH, temperature, and enzyme concentration during processing were 200 g/l, 5.5, 65°C, and 7.5 IU, respectively. In pre-treatment experiments, the concentration of enzymes and the pre-treatment temperature are highly correlated. The influence of pH, temperature, and substrate density on ethanol production was investigated. Temperature pH was determined as optimal, 32°C and 5.5, respectively. After 48 hours of fermentation at optimum pH, a solution of wheat bran containing a maximum of 6% starch produces a maximum of 22.9 g/l ethanol.展开更多
This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniquenes...This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.展开更多
Aiming at the problem of system error and noise in simultaneous localization and mapping(SLAM) technology, we propose a calibration model based on Project Tango device and a loop closure detection algorithm based on v...Aiming at the problem of system error and noise in simultaneous localization and mapping(SLAM) technology, we propose a calibration model based on Project Tango device and a loop closure detection algorithm based on visual vocabulary with memory management. The graph optimization is also combined to achieve a running application. First, the color image and depth information of the environment are collected to establish the calibration model of system error and noise. Second, with constraint condition provided by loop closure detection algorithm, speed up robust feature is calculated and matched. Finally, the motion pose model is solved, and the optimal scene model is determined by graph optimization method. This method is compared with Open Constructor for reconstruction on several experimental scenarios. The results show the number of model's points and faces are larger than Open Constructor's, and the scanning time is less than Open Constructor's. The experimental results show the feasibility and efficiency of the proposed algorithm.展开更多
A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality co...A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.展开更多
Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion function...Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.展开更多
This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is ...This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.展开更多
基金Sponsored by the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20092302120)
文摘In order to reduce the torque ripple,increase the average torque and optimize the drive performance of the switched reluctance motor (SRM),the nonlinear dynamic model of SRM is established in the MATLAB /Simulink environment.The effects of the turn-on and turn-off angles are investigated by the simulation results of the dynamic model,and the function is made among the rotor speed,turn-on angle and turn-off angle.To optimize the torque dynamic performance,the two-objective simultaneous optimization function is proposed by two weight factors.And the optimized turn-on and turn-off angles as functions of rotor speed are developed by using the simultaneous optimization method.Then the optimized torque controller is designed based on the optimized turn-on and turn-off angles.The simulation results show that the optimized torque controller designed in this paper can effectively reduce the torque ripple and increase the average torque,and optimize the torque dynamic performance of the SRM.
基金Supported by the National Natural Science Foundation of China （20976022） and Dalian University of Technology for Constructing Interdiscipline ＇Energy＋X＇. ACKNOWLEDGEMENTS The authors gratefully acknowledge financial support from Lanzhou Petrochemical Company, PetroChina Company Limited.
文摘A novel methodology is presented for simultaneously optimizing synthesis and cleaning schedule of flexible heat exchanger network(HEN)by genetic/simulated annealing algorithms(GA/SA).Through taking into account the effect of fouling process on optimal network topology,a preliminary network structure possessing two-fold oversynthesis is obtained by means of pseudo-temperature enthalpy(T-H)diagram approach prior to simultaneous optimization.Thus,the computational complexity of this problem classified as NP(Non-deterministic Polynomial)-complete can be significantly reduced.The promising matches resulting from preliminary synthesis stage are further optimized in parallel with their heat exchange areas and cleaning schedule.In addition,a novel continu- ous time representation is introduced to subdivide the given time horizon into several variable-size intervals according to operating periods of heat exchangers,and then flexible HEN synthesis can be implemented in dynamic manner.A numerical example is provided to demonstrate that the presented strategy is feasible to decrease the total annual cost(TAC)and further improve network flexibility,but even more important,it may be applied to solve large-scale flexible HEN synthesis problems.
基金Projects(61533021,61321003,61273185)supported by the National Natural Science Foundation of ChinaProject(2015CX007)supported by the Innovation-driven Plan in Central South University,ChinaProject(13JJ8003)supported by the Joint Fund of Hunan Provincial Natural Science Foundation of China
文摘Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their doses for the experiment are selected according to the characteristics of the zinc sulfate solution. Then, the reagent doses are optimized by analyzing the influence of reagent dose on the polarographic parameters(i.e. half-wave potential E_(1/2) and limiting diffusion current I_p). Finally, the optimization results are verified by simultaneously determining trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+). The determination results indicate that the optimized reagents exhibit wide linearity, low detection limits, high accuracy and good precision for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+).
基金supported by the National Natural Science Foundation of China(Nos.41004096 and 41230318)
文摘A new prestack AVA simultaneous inversion using particle swarm optimization algorithm is proposed, which can obtain the elastic parameters such as P-wave and S-wave impedance from P-wave reflection data simultaneously. Compared with the conventional AVA inversion based on generalized linear technique, this method does not depend on the initial model and can reach the global minimum. In order to increase the stability of the inversion, low-frequency trends of P-wave and S-wave impedances are built into the inversion. This method has been successfully applied to synthetic and field data. The estimated P-wave and S-wave impedances can be combined to derive other elastic parameters, which are sensitive for lithology identification and fluid prediction.
基金Supported by the Joint Funds of NSFC-CNPC of China(U1162130)the International Cooperation and Exchange Project of Science and Technology Department of Zhejiang Province(2009C34008)+1 种基金the National High Technology Research and Development Program of China(2006AA05Z226)the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists(R4100133)
文摘An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at dement knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refine- ment more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting dements to track optimal control profile breakpoints and ensure accurate state and centrol profiles. Four classic benchmarks of dynamic op- timization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferz,ble in improving the solution accuracy of chemical dy- namic optimization problem.
基金Supported by the National Natural Science Foundation of China(21276111,21206053,61305017)the Programme of Introducing Talents of Discipline to Universities(B12018)+2 种基金Fundamental Research Funds for the Central Universities(JUSRP11558)the Natural Science Foundation of Jiangsu Province(no.BK20160162)the Fundamental Research Funds for the Central Universities(JUSRP51510)
文摘Chinese rice wine making is a typical simultaneous saccharification and fermentation （SSF） process. During the fermentation process, temperature is one of the key parameters which decide the quality of Chinese rice wine. To optimize the SSF process for Chinese rice wine brewing, the effects of temperature on the kinetic parameters of yeast growth and ethanol production at various temperatures were determined in batch cultures using a mathematical model. The kinetic parameters as a function of temperature were evaluated using the software Origin8.0. Combing these functions with the mathematical model, an appropriate form of the model equations for the SSF considering the effects of temperature were developed. The kinetic parameters were found to fit the experimental data satisfactorily with the developed temperature-dependent model. The temperature profile for maximizing the ethanol production for rice wine fermentation was determined by genetic algorithm. The optimum temperature profile began at a low temperature of 26℃ up to 30 h. The operating temperature increased rapidly to 31.9 ℃, and then decreased slowly to 18℃ at 65 h. Thereafter, the temperature was maintained at 18 ℃ until the end of fermentation. A maximum ethanol production of 89.3 g.L 1 was attained. Conceivably, our model would facilitate the improvement of Chinese rice wine production at the industrial scale.
文摘This article attempts to develop a simultaneous optimization procedure of several response variables from incomplete multi-response experiments. In incomplete multi-response experiments all the responses (p) are not recorded from all the experimental units (n). Two situations of multi-response experiments considered are (i) on units all the responses are recorded while on units a subset of responses is recorded and (ii) on units all the responses (p) are recorded, on units a subset of responses is recorded and on units the remaining subset of responses is recorded. The procedure of estimation of parameters from linear multi-response models for incomplete multi-response experiments has been developed for both the situations. It has been shown that the parameter estimates are consistent and asymptotically unbiased. Using these parameter estimates, simultaneous optimization of incomplete multi-response experiments is attempted following the generalized distance criterion [1]. For the implementation of these procedures, SAS codes have been developed for both complete (k ≤ 5, p = 5) and incomplete (k ≤ 5, p1 = 2, 3 and p2 = 2, 3, where k is the number of factors) multi-response experiments. The procedure developed is illustrated with the help of a real data set.
基金Project (2002CB312200) supported by the National Key Basic Research and Development Program of China Project(03JJY3109) supported by the Natural Science Foundation of Hunan Province
文摘An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.
文摘The effects of process variables in Simultaneous Saccharification and Fermentation (SSF) of wheat bran flour were studied in bulk fermentation using a coculture of Aspergillus niger - Kluveromyces marxianus. The effect of substrate density, pH, temperature, and enzyme concentration on wheat bran was predicted by designing experiments in which a single parameter is varied keeping other variables at a constant level. The above parameters were optimized for a batch culture in a fermentor. Optimal values for substrate concentration, pH, temperature, and enzyme concentration during processing were 200 g/l, 5.5, 65°C, and 7.5 IU, respectively. In pre-treatment experiments, the concentration of enzymes and the pre-treatment temperature are highly correlated. The influence of pH, temperature, and substrate density on ethanol production was investigated. Temperature pH was determined as optimal, 32°C and 5.5, respectively. After 48 hours of fermentation at optimum pH, a solution of wheat bran containing a maximum of 6% starch produces a maximum of 22.9 g/l ethanol.
基金partially supported by PIP No.0534 from CONICET-Univ.AustralPPI No.18C417 from SECy T-UNRCpartially supported by AVENTURES-ANR-12-BLAN-BS01-0001-01
文摘This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.
基金Supported by the National Natural Science Foundation of China(61772379)
文摘Aiming at the problem of system error and noise in simultaneous localization and mapping(SLAM) technology, we propose a calibration model based on Project Tango device and a loop closure detection algorithm based on visual vocabulary with memory management. The graph optimization is also combined to achieve a running application. First, the color image and depth information of the environment are collected to establish the calibration model of system error and noise. Second, with constraint condition provided by loop closure detection algorithm, speed up robust feature is calculated and matched. Finally, the motion pose model is solved, and the optimal scene model is determined by graph optimization method. This method is compared with Open Constructor for reconstruction on several experimental scenarios. The results show the number of model's points and faces are larger than Open Constructor's, and the scanning time is less than Open Constructor's. The experimental results show the feasibility and efficiency of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China（20676117） the National Creative Research Groups Science Foundation of China（60421002）
文摘A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.
基金Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA).
文摘Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.
文摘This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.
