Publications
207 results found
RUSTEM B, 1995, COMPUTING OPTIMAL MULTI-CURRENCY MEAN-VARIANCE PORTFOLIOS, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 19, Pages: 901-908, ISSN: 0165-1889
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- Citations: 4
Rustem B, 1995, A discrete min-max algorithm: risk management with rival scenarios, Modelling and Control of National and Regional Economies, Pages: 353-364
Rustem B, 1995, The two-step and three-step Q-superlinear convergence of successive quadratic programming algorithms, Journal of Optimization Theory and Applications, Vol: 83, Pages: 613-619
RUSTEM B, 1994, 2-STEP AND 3-STEP Q-SUPERLINEAR CONVERGENCE OF SQP METHODS, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 83, Pages: 613-619, ISSN: 0022-3239
RUSTEM B, 1994, STOCHASTIC AND ROBUST-CONTROL OF NONLINEAR ECONOMIC-SYSTEMS, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 73, Pages: 304-318, ISSN: 0377-2217
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- Citations: 13
Rustem B, 1994, Interactive decision making: Equivalence of modified formulations, Annals of Operations Research, Vol: 51, Pages: 1-13, ISSN: 0254-5330
We discuss the use of a quadratic norm for departures from the bliss value of a decision problem under conflicting objectives. The use of a quadratic norm is, for example, of interest within the dynamic framework of optimal control. The symmetric nature of the quadratic norm is relaxed to allow for nonsymmetric preferences. The possibility of tailoring the quadratic objective function to generate optimal policies which are acceptable to the policy maker is explored with two alternative interactive algorithms. One of these is for objective functions with diagonal weighting matrices and uses updates of the bliss values. The second algorithm proceeds by updating non-diagonal weights, while keeping the bliss values fixed. The equivalence of both algorithms is established. © 1994 J.C. Baltzer AG, Science Publishers.
BECKER R, HALL S, RUSTEM B, 1994, ROBUST OPTIMAL DECISIONS WITH STOCHASTIC NONLINEAR ECONOMIC-SYSTEMS, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 18, Pages: 125-147, ISSN: 0165-1889
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- Citations: 16
Howe M, Rustem B, Selby M, 1994, Minimax hedging strategy, Computational Economics, Vol: 7, Pages: 245-275
Rustem B, 1994, Convergent stepsizes for constrained min-max algorithms, Advances in dynamic games and applications (Geneva, 1992), Publisher: BIrkhauser Boston, Pages: 168-194
RUSTEM B, 1994, CONVERGENT STEPSIZES FOR CONSTRAINED MIN-MAX ALGORITHMS, Biannual Symposium of ISDG: Advances in Dynamic Games and Applications, Publisher: BIRKHAUSER BOSTON, Pages: 168-194
Rustem B, 1994, Two-step and three-step Q-superlinear convergence of {SQP} methods, Journal of Optimization Theory and Applications, Vol: 83, Pages: 613-619
Rustem B, 1994, Stochastic and robust control of nonlinear economic systems, European Journal of Operations Research, Vol: 73, Pages: 304-318
Rustem B, 1994, A Discrete min-max algorithm for inequality constraints, Operations Research '93, Pages: 428-430
Rustem B, 1994, Interactive decision making: Equivalence of modified formulations, Annals of Operations Research, Vol: 51, Pages: 3-13
Becker R, Rustem B, 1993, Algorithms for solving nonlinear dynamic decision models, Annals of Operations Research, Vol: 44, Pages: 115-142, ISSN: 0254-5330
In this paper we discuss two Newton-type algorithms for solving economic models. The models are preprocessed by reordering the equations in order to minimize the dimension of the simultaneous block. The solution algorithms are then applied to this block. The algorithms evaluate numerically, as required, selected columns of the Jacobian of the simultaneous part. Provisions also exist for similar systems to be solved, if possible, without actually reinitialising the Jacobian. One of the algorithms also uses the Broyden update to improve the Jacobian. Global convergence is maintained by an Armijo-type stepsize strategy. The global and local convergence of the quasi-Newton algorithm is discussed. A novel result is established for convergence under relaxed descent directions and relating the achievement of unit stepsizes to the accuracy of the Jacobian approximation. Furthermore, a simple derivation of the Dennis-Moré characterisation of the Q-superlinear convergence rate is given. The model equation reordering algorithm is also described. The model is reordered to define heart and loop variables. This is also applied recursively to the subgraph formed by the loop variables to reduce the total number of above diagonal elements in the Jacobian of the complete system. The extension of the solution algorithms to consistent expectations are discussed. The algorithms are compared with Gauss-Seidel SOR algorithms using the USA and Spanish models of the OECD Interlink system. © 1993 J.C. Baltzer AG, Science Publishers.
RUSTEM B, 1993, EQUALITY AND INEQUALITY CONSTRAINED OPTIMIZATION ALGORITHMS WITH CONVERGENT STEPSIZES, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 76, Pages: 429-453, ISSN: 0022-3239
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- Citations: 8
Becker R, Rustem B, 1993, Algorithms for solving nonlinear dynamic decision models, Annals of Operations Research, Vol: 44, Pages: 117-142, ISSN: 0254-5330
Rustem B, 1992, A constrained min-max algorithm for rival models of the same economic system, Mathematical Programming, Vol: 53, Pages: 279-295, ISSN: 0025-5610
There are well-established rival theories about the economy. These have, in turn, led to the development of rival models purporting to represent the economic system. The models are large systems of discrete-time nonlinear dynamic equations. Observed data of the real system does not, in general, provide sufficient information for statistical methods to invalidate all but one of the rival models. In such a circumstance, there is uncertainty about which model to use in the formulation of policy. Prudent policy design would suggest that a model-based policy should take into account all the rival models. This is achieved as a pooling of the models. The pooling that yields the policy which is robust to model choice is formulated as a constrained min-max problem. The minimization is over the decision variables and the maximization is over the rival models. Only equality constraints are considered.\r\n\r\nA successive quadratic programming algorithm is discussed for the solution of the min-max problem. The algorithm uses a stepsize strategy based on a differentiable penalty function for the constraints. Two alternative quadratic subproblems can be used. One is a quadratic min-max and the other a quadratic programming problem. The objective function of either subproblem includes a linear term which is dependent on the penalty function. The penalty parameter is determined at every iteration, using a strategy that ensures a descent property as well as the boundedness of the penalty term. The boundedness follows since the strategy is always satisfied for finite values of the parameter which needs to be increased a finite number of times.\r\n\r\nThe global and local convergence of the algorithm is established. The conditions, involving projected Hessian approximations, are discussed under which the algorithm achieves unit stepsizes and subsequently Q-superlinear convergence.
PARASKEVOPOULOS D, KARAKITSOS E, RUSTEM B, 1991, ROBUST CAPACITY PLANNING UNDER UNCERTAINTY, MANAGEMENT SCIENCE, Vol: 37, Pages: 787-800, ISSN: 0025-1909
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- Citations: 77
RUSTEM B, 1991, THE DIAGONALIZABILITY OF QUADRATIC-FUNCTIONS AND THE ARBITRARINESS OF SHADOW PRICES, AUTOMATICA, Vol: 27, Pages: 573-578, ISSN: 0005-1098
Rustem B, 1991, Superlinear convergence of successive quadratic programming algorithms, IFAC Symposia Series - Proceedings of a Triennial World Congress, Vol: 3, Pages: 397-402
Convergence rate conditions are considered for sequential quadratic programming algorithms for equality and inequality constraints. The objective function of the quadratic subproblem includes a linear term that is dependent on constraint penalty functions and an approximate Hessian of the Lagrangian augmented by the penalty functions. The penalty function contribution in the linear term ensures the consistency of the algorithm before and after unit stepsizes have been attained. Conditions which ensure the Q - and two-step Q- superlinear convergence of {xk} are discussed along with the rates of the multipliers of the equality and inequality constraints. The convergence rate of these multipliers may be important when, for example, they are interpreted as shadow prices in decision making problems. Furthermore, the penalty parameters may affect the multipliers. It is shown that the sequences {xk, λk}, {k$/, λk, μk} including the multipliers in general converge more slowly than {xk}. It is also shown that the inequality constraints increase the complexity of the problem. In the context of the proposed algorithm, the simple treatment of the active constraints at the solution as equalities appears to be insufficient. Except in one case, however, inequality constraints do not deteriorate the convergence rates any more than equality constraints.
Rustem B, 1991, The diagonalizability of quadratic functions and the arbitrariness of shadow prices, Automatica. A Journal of IFAC, the International Federation ofAutomatic Control, Vol: 27, Pages: 573-578, ISSN: 0005-1098
RUSTEM B, VELUPILLAI K, 1990, RATIONALITY, COMPUTABILITY, AND COMPLEXITY, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 14, Pages: 419-432, ISSN: 0165-1889
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- Citations: 8
Rustem B, 1990, Methods for optimal economic policy design, Publisher: Academic Press, Pages: 17-74
Rustem B, 1989, Robust optimal policy methods for nonlinear models, Publisher: IEEE, Pages: 2050-2055
RUSTEM B, 1989, A SUPERLINEARLY CONVERGENT CONSTRAINED MIN-MAX ALGORITHM FOR RIVAL MODELS OF THE SAME SYSTEM, COMPUTERS & MATHEMATICS WITH APPLICATIONS, Vol: 17, Pages: 1305-1316, ISSN: 0898-1221
RUSTEM B, 1988, A CONSTRAINED MIN-MAX ALGORITHM FOR RIVAL MODELS, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 12, Pages: 101-107, ISSN: 0165-1889
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- Citations: 2
RUSTEM B, VELUPILLAI K, 1987, OBJECTIVE FUNCTIONS AND THE COMPLEXITY OF POLICY DESIGN, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 11, Pages: 185-192, ISSN: 0165-1889
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- Citations: 2
BECKER RG, DWOLATZKY B, KARAKITSOS E, et al., 1986, THE SIMULTANEOUS USE OF RIVAL MODELS IN POLICY OPTIMIZATION, ECONOMIC JOURNAL, Vol: 96, Pages: 425-448, ISSN: 0013-0133
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- Citations: 13
BECKER RG, DWOLATZKY B, KARAKITSOS E, et al., 1986, OPTIMAL POLICY DESIGN WITH NONLINEAR MODELS - THE MULTIAGENT CASE, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 10, Pages: 27-31, ISSN: 0165-1889
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- Citations: 2
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