Publications
207 results found
Kriwaczek F, Rustem B, 2000, Interactive multi-attribute decision making, based on quadratic programming, Departmental Technical Report: 2000/17, Publisher: Department of Computing, Imperial College London
In order to make a decision in the face of multiple objectives it is necessary to know the relative importance of the different objectives. Yet, it is often very difficult to specify a set of precise weights before possible alternatives solutions are known. In this paper, we present an interactive, iterative method for arriving at an acceptable solution. The decision maker gradually discerns what is achievable and adjusts his aspirations and (implicitly) the specification of weights and trade-offs between his objectives, in the light of what he learns. To aid the decision maker's cognition and to allow him to express his wishes in a natural way, we employ an intuitive interface, based on the parallel coordinates method of displaying and specifying points in multidimensional space.
Rustem B, Becker RG, Marty W, 2000, Robust min-max portfolio strategies for rival forecast and risk scenarios, JOURNAL OF ECONOMIC DYNAMICS & CONTROL, Vol: 24, Pages: 1591-1621, ISSN: 0165-1889
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- Citations: 33
Akrotirianankis I, Maros I, Rustem B, 2000, An outer approximation based branch and cut algorithm for convex 0-1 MINLP problems, Departmental Technical Report: 2000/6, Department of Computing, Imperial College London
A branch and cut algorithm is developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints are linearized at the optimum solution of those NLP problems and the linearizations are added to all the unsolved nodes of the enumerations tree. Also, Gomory cutting planes, which are valid throughout the tree, are generated at selected nodes. These cuts help the algorithm to locate integer solutions quickly and consequently improve the linear approximation of the objective and constraints, held at the unsolved nodes of the tree. Numerical results show that the addition of Gomory cuts can reduce the number of nodes in the enumeration tree.
Kontoghiorghes EJ, Nagurney A, Rustem B, 2000, Parallel computing in economics, finance and decision-making, PARALLEL COMPUTING, Vol: 26, Pages: 507-509, ISSN: 0167-8191
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- Citations: 8
Darlington J, Pantelides CC, Rustem B, et al., 2000, Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 121, Pages: 343-362, ISSN: 0377-2217
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- Citations: 28
Akrotirianakis I, Rustem B, 2000, A primal-dual interior point algorithm with an exact and differentiable merit function for nonlinear programming, Optimization Methods and Software, Pages: 1-36
Zakovic S, Pantelides C, Rustem B, 2000, An interior point algorithm for computing saddle points of constrained continuous minimax, ANNALS OF OPERATIONS RESEARCH, Vol: 99, Pages: 59-77, ISSN: 0254-5330
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- Citations: 20
Kontoghiorghes E, Nagurney A, Rustem B, 2000, Special issue: Parallel Computing in Economics, Finance and Decision Making, Parallel Computing
Akrotirianakis I, Rustem B, 2000, A primal-dual interior point algorithm with an exact and differentiable merit function for nonlinear programming, International Conference on Nonlinear Programming and Variational Inequalities, Publisher: GORDON BREACH SCI PUBL LTD, Pages: 1-36, ISSN: 1055-6788
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- Citations: 4
Darlington J, Pantelides CC, Rustem B, et al., 2000, An efficient approximate algorithm for optimal decisions under uncertainty, European Journal of Operations Research, Vol: 121, Pages: 343-362
Akrotirianakis I, Maros I, Rustem B, 2000, An Outer Approximation Based Branch And Cut Algorithm For Convex 0-1 Minlp Problems, Departmental Technical Reports, 6
Akrotirianakis I, Maros I, Rustem B, 2000, An Outer Approximation Based Branch And Cut Algorithm For Convex 0-1 Minlp Problems, Departmental Technical Reports, 6
Akrotirianakis I, Rustem B, 1999, A primal-dual interior point algorithm that uses an exact and differentiable merit function to solve general nonlinear problems, Departmental Technical Report: 98/9, Publisher: Department of Computing, Imperial College London
A primal-dual interior point algorithm for solving general nonlinear programming problems is presented. The algorithm solves the perturbed optimality conditions by applying a quasi-Newton method, where the Hessian of the Lagrangian is replaced by a positive definite approximation. An approximation of Fletcher's exact and differentiable merit function together with line-search procedures are incorporated into the algorithm. The line-search procedures are used to modify the length of the step so that the value of the merit function is always reduced. Different step-sizes are used for the primal and dual variables. The search directions are ensured to be descent for the merit function, which is thus used to guide the algorithm to an optimum solution of the constrained optimisation problem. The monotonic decrease of the merit function at each iteration ensures the global convergence of the algorithm. Finally, preliminary numerical results demonstrate the efficient performance of the algorithm for a variety of problems.
Darlington J, Pantelides CC, Rustem B, et al., 1999, An algorithm for constrained nonlinear optimization under uncertainty, AUTOMATICA, Vol: 35, Pages: 217-228, ISSN: 0005-1098
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- Citations: 48
Rustem B, Nguyen Q, 1998, An algorithm for the inequality-constrained discrete min-maxproblem, SIAM Journal on Optimization, Pages: 265-283, ISSN: 1052-6234
Pinto RLV, Rustem B, 1998, Solving a mixed-integer multiobjective bond portfolio model involving logical conditions, Seminar on Applied Mathematical Programming and Modelling (APMOD 95), Publisher: BALTZER SCI PUBL BV, Pages: 497-513, ISSN: 0254-5330
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- Citations: 2
Tanyi BA, Rustem B, Darlington J, 1998, Parallelisation of a nonlinear robust optimization algorithm, Parallel Computing: Fundamentals, Applications and New Directions, Publisher: Elsevier Science BV, Pages: 171-178
Rustem B, 1998, Learning in Multiple objective decision making, Apprentisage, des Principe Naturels aux Modeles Artificiels, Paris, Pages: 205-218
Rustem B, Nguyen Q, 1998, An algorithm for the inequality constrained discrete min-max problem, SIAM J Optimization, Vol: 8, Pages: 265-283
Rustem B, 1998, Algorithms for Nonlinear Programming and Multiple Objective Decisions, Publisher: John Wiley & Sons, ISBN: 9780471978503
Rustem B, Howe M, 1998, An approach to continuous minimax, the basic algorithm, Computation in Economics, Finance and Engineering-Economic Systems
Rustem B, Pinto R, 1998, Solving a mixed-integer multiobjective bond portfolio model involving logical conditions, Annals of Operations Research, Vol: 81, Pages: 497-513, ISSN: 0254-5330
Akrotirianakis I, Rustem B, 1997, A globally convergent primal-dual interior point algorithm for general non-linear programming, Departmental Technical Report: 97/14, Department of Computing, Imperial College London
This paper presents a primal-dual interior point algorithm for solving general constrained non-linear programming problems. The initial problem is transformed to an equivalent equality constrained problem, with inequality constraints incorporated into the objective function by means of a logarithmic barrier function. Satisfaction of the equality constraints is enforced through the incorporation of an adaptive quadratic penalty function into the objective. The penalty parameter is determined using a strategy that ensures a descent property for a merit function. It is shown that the adaptive penalty does not grow indefinitely. The algorithm applies Newton's method to solve the first order optimality conditions of the equivalent equality problem. Global convergence of the algorithm is achieved through the monotonic decrease of a merit function. Locally the algorithm is shown to be quadratically convergent.
Howe MA, Rustem B, 1997, A robust hedging algorithm, 1st Meeting of the Society-of-Computational-Economics, Publisher: ELSEVIER SCIENCE BV, Pages: 1065-1092, ISSN: 0165-1889
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- Citations: 10
Howe M, Rustem B, 1997, A robust hedging algorithm, Journal of Economic Dynamics and Control, Vol: 21, Pages: 1065-1092, ISSN: 0165-1889
Tanyi B, Darlington J, Pantelides C, 1997, Robust optimisation of nonlinear systems under parametric uncertainty, Publisher: Springer, Pages: 43-48
Rustem B, Amman H, Whinston A, 1997, Computational approaches to economic problems, Publisher: Kluwer Academic Publishers, ISBN: 9780792343974
Howe MA, Rustem B, Selby MJP, 1996, Multi-period minimax hedging strategies, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 93, Pages: 185-204, ISSN: 0377-2217
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- Citations: 13
Tanyi BA, Darlington J, Pantelides CC, et al., 1996, Robust optimization of nonlinear systems under parametric uncertainty, Proceedings of Operations Research, Publisher: Springer Verlag, Pages: 43-54
Pinto RLV, Rustem B, 1996, Building and solving multi-criteria models involving logical conditions, Advances in Computational Economics, Editors: Gilli, Publisher: Kluwer, Pages: 123-138
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