This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program ...This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.展开更多
The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are us...The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.展开更多
In this work, three decentralized control configuration designs—independent, sequential and simultaneous designs—were used in multivariable feedback configurations for PI control of the riser and regenerator tempera...In this work, three decentralized control configuration designs—independent, sequential and simultaneous designs—were used in multivariable feedback configurations for PI control of the riser and regenerator temperatures of FCCU in order to compare their performances. Control design was formulated as optimization problem to minimize infinity norm of weighted sensitivity functions subject to μ-interaction measure bound on diagonal complementary functions of the closed loop system. The optimization problem was solved using augmented Lagrangian genetic algorithm. Simulation results show that simultaneous and independent designs give good response with less overshoot and with no oscillation. Bound on μ-interaction measure is satisfied for both designs meaning that their nominal stabilities are guaranteed;however, it is marginal for simultaneous design. Simultaneous design outperforms independent design in term of robust performance while independent design gives the best performance in terms of robust stability. Sequential design gives the worst performance out of the three designs.展开更多
In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The maj...In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation,which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation.Some computational results are included.Computation results indicate that the algorithm can solve fairly large scale problems.展开更多
In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization prob...In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.展开更多
基金supported by the Chinese Natural Science Foundation under Grant Nos.11571271,11331012,71331001,11631013the National Funds for Distinguished Young Scientists under Grant No.11125107the National 973 Program of China under Grant No.2015CB856000
文摘This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.
文摘The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.
文摘In this work, three decentralized control configuration designs—independent, sequential and simultaneous designs—were used in multivariable feedback configurations for PI control of the riser and regenerator temperatures of FCCU in order to compare their performances. Control design was formulated as optimization problem to minimize infinity norm of weighted sensitivity functions subject to μ-interaction measure bound on diagonal complementary functions of the closed loop system. The optimization problem was solved using augmented Lagrangian genetic algorithm. Simulation results show that simultaneous and independent designs give good response with less overshoot and with no oscillation. Bound on μ-interaction measure is satisfied for both designs meaning that their nominal stabilities are guaranteed;however, it is marginal for simultaneous design. Simultaneous design outperforms independent design in term of robust performance while independent design gives the best performance in terms of robust stability. Sequential design gives the worst performance out of the three designs.
基金Foundation item： Supported by the National Natural Science Foundation of China（10726016） Supported by the Hubei Province Natural Science Foundation Project（T200809 D200613002）
文摘In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation,which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation.Some computational results are included.Computation results indicate that the algorithm can solve fairly large scale problems.
文摘In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.
