In this paper, we study linear programming problems with both the cost and right-hand-side vectors being stochastic. Kalman filtering techniques are integrated into the infeasible interior-point method to develop an o...
详细信息
In this paper, we study linear programming problems with both the cost and right-hand-side vectors being stochastic. Kalman filtering techniques are integrated into the infeasible interior-point method to develop an on-line algorithm. We first build a ''noisy dynamic model'' based on the Newton equation developed in the infeasible-interior-point method. Then, we use Kalman filtering techniques to filter out the noise for a stable direction of movement. Under appropriate assumptions, we show a new result of the limiting property of Kalman filtering in this model and prove that the proposed on-line approach is globally convergent to a ''true value solution'' in the mode of quadratic mean.
This paper provides a theoretical framework of dependent-chance programming, as well as dependent-chance multiobjective programming and dependent-chance goal programming which are new types of stochastic optimization....
详细信息
This paper provides a theoretical framework of dependent-chance programming, as well as dependent-chance multiobjective programming and dependent-chance goal programming which are new types of stochastic optimization. A stochastic simulation based genetic algorithm is also designed for solving dependent-chance programming models.
This paper further discusses the techniques of dependent-chance programming, dependent-chance multiobjective programming and dependent-chance goal programming. Some illustrative examples are provided to show how to mo...
详细信息
This paper further discusses the techniques of dependent-chance programming, dependent-chance multiobjective programming and dependent-chance goal programming. Some illustrative examples are provided to show how to model complex stochastic decision systems by using dependent-chance programming and how to serve these models by employing a Monte Carlo simulation based genetic algorithm. (C) 1997 Elsevier Science B.V.
Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainy in the timing and amount of cashflows, changes in the de...
详细信息
Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainy in the timing and amount of cashflows, changes in the default and other risk premia and so on, complicate the portfolio manager's problem. We develop here a multi-period, dynamic, portfolio optimization model to address this problem. The model specifies a sequence of investment decisions over time that maximize the expected utility of return at the end of the planning horizon. The model is a two-stage stochastic program with recourse. The dynamics of interest rates, cashflow uncertainty, and liquidity, default and other risk premia, are explicitly modeled through postulated scenarios. Simulation procedures are developed to generate these scenarios, The optimization models are then integrated with the simulation procedures. Extensive validation experiments are carried out to establish the effectiveness of the model in dealing with uncertainty. In particular the model is compared against the popular portfolio immunization strategy, and against a portfolio based on mean-absolute deviation optimization.
The stochastic linear programming problem with recourse has a dual block-angular structure. II can thus be handled by Benders' decomposition or by Kelley's method of cutting planes;equivalently the dual proble...
详细信息
The stochastic linear programming problem with recourse has a dual block-angular structure. II can thus be handled by Benders' decomposition or by Kelley's method of cutting planes;equivalently the dual problem has a primal block-angular structure and can be handled by Dantzig-Wolfe decomposition-the two approaches are in fact identical by duality. Here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations. The only significant difference form the aforementioned methods is that new cutting planes (or columns, by duality) will be generated not from the optimum of the linear programming relaxation, but from the analytic center of the set of localization.
Extended Linear-Quadratic programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence...
详细信息
Extended Linear-Quadratic programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence rates have been developed for solving fully quadratic ELQP problems, where the primal and dual coefficient matrices are positive definite. We present a two-stage sequential quadratic programming (SQP) method for solving ELQP problems arising in stochastic programming. The first stage algorithm realizes global convergence and the second stage algorithm realizes superlinear local convergence under a condition called B-regularity. B-regularity is milder than the fully quadratic condition;the primal coefficient matrix need not be positive definite. Numerical tests are given to demonstrate the efficiency of the algorithm. Solution properties of the ELQP problem under B-regularity are also discussed.
A new heuristic approach for stochastic programming Problems (SPP) is presented. Here the heuristic idea is based on an analogy of SPP with the problem of determination of the centre of gravity in certain physical sys...
详细信息
A new heuristic approach for stochastic programming Problems (SPP) is presented. Here the heuristic idea is based on an analogy of SPP with the problem of determination of the centre of gravity in certain physical systems. A general purpose algorithm is presented for SPPs with discrete random coefficients. An analysis of the efficiency and reliability of this heuristic approach is presented along with computational results on some test problems.
This paper considers stochastic linear programming models for production planning where cost coefficient and RHS term uncertainties are represented by finite discrete probability distribution functions. The solution o...
详细信息
This paper considers stochastic linear programming models for production planning where cost coefficient and RHS term uncertainties are represented by finite discrete probability distribution functions. The solution of the two-stage fixed recourse problem is considered, for which a sensitivity-based successive disaggregation algorithm is proposed. The bounding properties of the aggregate sub-problems are examined in the context of the disaggregation algorithm. The partitioning algorithm converges to the exact solution in a finite number of iterations, and has a highly parallel decomposition and computer implementation. Example problems for the two-stage case are presented to demonstrate the solution technique. Results are compared with the alternative solution methods, variants of Benders decomposition schemes tailored to the dynamic staircase LP structure. Theoretical properties of the algorithm are examined, and several example problems are solved where the certainty equivalent problem involves millions of variables and constraints. (C) 1997 Elsevier Science Ltd.
In this paper we are concerned with stochastic optimization problems in the case when the joint probability distribution, associated with random parameters, can be described by means of a Bayesian net, In such a case ...
详细信息
In this paper we are concerned with stochastic optimization problems in the case when the joint probability distribution, associated with random parameters, can be described by means of a Bayesian net, In such a case we suggest that the structured nature of the probability distribution can be exploited for designing efficient gradient estimation algorithm. Such gradient estimates can be used within the general framework of stochastic gradient (quasi-gradient) solution procedures in order to solve complex non-linear stochastic optimization problems. We describe a gradient estimation algorithm and present a case study related to the reliability of semiconductor manufacturing together with numerical experiments. (C) 1997 Published by Elsevier Science B.V.
This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of...
详细信息
This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of random variables is widespread. We introduce algorithms to find upper bounds on the optimal value of two-stage and multi-stage stochastic (minimization) programs with Gaussian right-hand sides. The upper bounds are obtained by solving deterministic mathematical programming problems with dimensions that do not depend on the sample space size. The algorithm for the two-stage problem involves the solution of a deterministic linear program and a simple semidefinite program. The algorithm for the multi-stage problem involves the solution of a quadratically constrained convex programming problem. (C) 1997 The Mathematical programming Society, Inc.
暂无评论