In this paper, we present a mathematical framework for the problem of minimizing the cash-out penalties of a natural gas shipper. The problem is modeled as a mixed-integer bilevel programming problem having one Boolea...
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In this paper, we present a mathematical framework for the problem of minimizing the cash-out penalties of a natural gas shipper. The problem is modeled as a mixed-integer bilevel programming problem having one Boolean variable in the lower level problem. Such problems are difficult to solve. To obtain a more tractable problem we move the Boolean variable from the lower to the upper level problem. The implications of this change of the problem are investigated thoroughly. The resulting lower level problem is a generalized transportation problem. The formulation of conditions guaranteeing the existence of an optimal solution for this problem is also in the scope of this paper. The corresponding results are then used to find a bound on the optimal function value of our initial problem. (c) 2004 Published by Elsevier B.V.
The subsonic airliner design is a difficult optimization problem because of adistorted design space and an unstable analysis tool. The limitations were overcome through acascade algorithm along with neural-network and...
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The subsonic airliner design is a difficult optimization problem because of adistorted design space and an unstable analysis tool. The limitations were overcome through acascade algorithm along with neural-network and regression method. The optimum solution was obtainedfor the real-world industrial problem. The optimum aircraft weight calculated by theflight-optimization system analyzer and the regression-method approximation matched well. Thedeviation in the design variables between the two analyzers was not significant. The overallperformance of neural-network and regression method was comparable. The neural network followed amean path, whereas the regression method closely followed the aircraft analyzer. For a singleanalysis cycle the aircraft-analyzer time measured in seconds is reduced to milliseconds by theapproximators. The training, validation, and solution required a small fraction of the aircraftanalysis and design time. For design optimization the central processing unit time with the aircraftanalyzer measured in hours, reduced to minutes by the neural network, and seconds by the regressionmethod.
The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors ...
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The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors conjectured that the CPLD could be a constraint qualification. This conjecture is proven in the present paper. Moreover, it is shown that the CPLD condition implies the quasinormality constraint quali. cation, but that the reciprocal is not true. Relations with other constraint quali. cations are given.
This paper presents an efficient approach based on a recurrent neural network for solving constrained nonlinear optimization. More specifically, a modified Hopfield network is developed, and its internal parameters ar...
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This paper presents an efficient approach based on a recurrent neural network for solving constrained nonlinear optimization. More specifically, a modified Hopfield network is developed, and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it handles optimization and constraint terms in different stages with no interference from each other. Moreover, the proposed approach does not require specification for penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyse its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.
Mathematical programming provides general tools for engineering design optimization. We present numerical models for simultaneous analysis and design optimization (SAND) and multidisciplinary design optimization (MDO)...
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Mathematical programming provides general tools for engineering design optimization. We present numerical models for simultaneous analysis and design optimization (SAND) and multidisciplinary design optimization (MDO) represented by mathematical programs. These models are solved with numerical techniques based on the feasible arc interior point algorithm (FAIPA) for nonlinear constrained optimization, Even if MDO is a very large optimization problem, our approach reduces considerably the computer effort. Several took for very large problems are also presented. The present approach is very strong and efficient for real industrial applications and can easily interact with existing simulation engineering codes. (c) 2005 Elsevier B.V. All rights reserved.
Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems wit...
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse. Second derivatives are assumed to be unavailable or too expensive to calculate. We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. The Hessian of the Lagrangian is approximated using a limited-memory quasi-Newton method. SNOPT is a particular implementation that uses a reduced-Hessian semidefinite QP solver (SQOPT) for the QP subproblems. It is designed for problems with many thousands of constraints and variables but is best suited for problems with a moderate number of degrees of freedom (say, up to 2000). Numerical results are given for most of the CUTEr and COPS test collections (about 1020 examples of all sizes up to 40000 constraints and variables, and up to 20000 degrees of freedom).
Part II is devoted to the formulation of the problem and models and methods of design of optimal logical structures for object-oriented databases used in designing automatic information control systems. The effectiven...
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Part II is devoted to the formulation of the problem and models and methods of design of optimal logical structures for object-oriented databases used in designing automatic information control systems. The effectiveness criteria used for the problem design are defined by the minimal total time of utilization of databases and service of a given set of user inquires and transactions, minimal total time of implementation of a set of inquires and transactions over the database. Design problems are formulated as nonlinear integer programming problems and effective exact and heuristic algorithms are developed to solve them.
Let K be a convex polyhedron in R-n with non-empty interior, and P-1, P-2,..., P-m, m >= n + 1, are vertices of K. Then K is the union of finite number of n-dimensional simplices {Sigma(n+1)(i=1)t(i) P-ji : t(i) &g...
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Let K be a convex polyhedron in R-n with non-empty interior, and P-1, P-2,..., P-m, m >= n + 1, are vertices of K. Then K is the union of finite number of n-dimensional simplices {Sigma(n+1)(i=1)t(i) P-ji : t(i) >= 0, Sigma(n+1)(i=1) t(i) = 1} for which the convex hull of the (n - 1)-dimensional circumscribed sphere of vertices P-j1, P-j2,..., Pjn+1 contains K. The result is applied to solve a linear programming problem concerning the circumscribed sphere of a convex polyhedron. (c) 2005 Elsevier Ltd. All rights reserved.
This paper shows that line losses can be accounted for locally in dc optimal power flow (DC-OPF) by adding rotated quadratic cones to a variation of the original linear set of constraints. The result is a conic quadra...
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This paper shows that line losses can be accounted for locally in dc optimal power flow (DC-OPF) by adding rotated quadratic cones to a variation of the original linear set of constraints. The result is a conic quadratic optimization problem. A favorable property of this problem is that primal-dual interior-point methods developed for linear programming can be generalized to its solution while maintaining their efficiency. Numerical results using an efficient implementation of an interior-point method are presented.
Electrodynamic tethers provide an efficient means for performing orbital transfers. In particular, the relatively new propellantless technology allows systems to be transferred from one orbit to another by simply modu...
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Electrodynamic tethers provide an efficient means for performing orbital transfers. In particular, the relatively new propellantless technology allows systems to be transferred from one orbit to another by simply modulating the level of electric current in the long, conducting tether. Because the tether is traveling through the Earth's magnetic field at high velocity, an electromotive force is generated that can alter the spacecraft's orbit. However, the force generated in the tether is a vector product of the Earth's magnetic field and the local direction of the conducting tether, which generates a Lorentz force perpendicular to both the tether and the magnetic field. This means that careful control of the current is necessary to effect desired changes to the spacecraft orbit. Various studies have been undertaken on the use of electrodynamic tethers to perform orbit transfers. For example, Johnson and Herrmann and Vas et al considered reboosting the orbit of the International Space Station using electrodynamic tethers. Hoyt and Forward3 designed the terminator tether system, which is capable of autonomously deorbiting small satellites. Lanoix et al studied the influence of electromagnetic forces on the orbital motion of tethered satellites and considered a very simple control scheme to alleviate the buildup of large-amplitude tether librations. Similarly, Hoyt has introduced feedback control to keep the tether librations within suitably selected bounds. More recently, Tragesser and San designed a guidance control methodology to transfer an electrodynamic tether system between selected orbits. However, it was assumed that the tether remains pointed along the local vertical (i.e., there are no tether librations), and bounds on the control current were not explicitly enforced. The control methodology used by Tragesser and San is based on the linear combination of current controls necessary to yield secular changes in each of the orbital elements. In this Note, the wor
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