作者：
Sellami, MohamedUniv Gabes
Natl Engn Sch Gabes Res Unit Mechan Modeling Energy & Mat M2EM Gabes 6029 Tunisia Univ Gabes
Natl Engn Sch Gabes Dept Civil Engn Gabes 6029 Tunisia
This paper presents a novel descent algorithm based on the step-by-step iterative principle, applied to the optimum design of steel frames. The search consists on finding the direction which decreases the structural w...
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This paper presents a novel descent algorithm based on the step-by-step iterative principle, applied to the optimum design of steel frames. The search consists on finding the direction which decreases the structural weight most quickly. As the design problem includes discrete variables, the optimum is found by evaluating the structural weight gradient step by step. The step size is controlled in such a way that convergence towards infeasible or suboptimal solutions is avoided. By properly choosing the initial solution, it is possible to increase the efficiency and the convergence speed of the algorithm. Many strategies, for the choice of initial design point, by making use of engineering intuitions or using optimized design obtained by other algorithms are discussed. Furthermore, it is confirmed in this study that the proposed algorithm can be used to improve optimum designs found by metaheuristic algorithms. The optimization results, relative to several weight minimizations problems of benchmark planar steel frames designed according to Load and Resistance Factor Design, American Institute of Steel Construction (LRFD-AISC) specifications, are compared to those obtained by different optimization methods. The comparison proves the efficiency and robustness as well as the prompt of convergence of the proposed descent algorithm developed in this paper.
We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are . Als...
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We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are . Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.
For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and p...
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For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the Generalized Eigenvalue Complementarity Problem (GEiCP) derived from unilateral friction elastic systems. Numerical experiments show the efficiency of the proposed methods compared to the projected steepest descent method with less CPU time.
In this paper, we focus on the problem of blind source separation (BSS). To solve the problem efficiently, a new algorithm is proposed. First, a parallel variable dual-matrix model (PVDMM) that considers all the numer...
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In this paper, we focus on the problem of blind source separation (BSS). To solve the problem efficiently, a new algorithm is proposed. First, a parallel variable dual-matrix model (PVDMM) that considers all the numerical relations between a mixing matrix and a separating matrix is proposed. Different constrained terms are used to construct the cost function for every sub-algorithm. These constrained terms reflect a numerical relation. Therefore, a number of undesired solutions are excluded, the search region is reduced, and the convergence efficiency of the algorithm is ultimately improved. Parallel sub-algorithms are proven to converge to a separable matrix only if the cost function approaches zero. Second, a descent algorithm (DA) as a PVDMM optimizing approach is proposed in this paper as well. Apparently, the efficiency of the algorithm depends completely on the DA. Unlike the traditional descent method, the DA defines step length by solving inequality instead of merely utilizing the Wolfe- or Armijo-type search rule. Stimulation results indicate that the DA can improve computational efficiency. Under mild conditions, the DA has been proven to have strong convergence properties. Numerical results also show that the method is very efficient and robust. Finally, we applied the combinative algorithm to the BSS problem. Computer simulations illustrate its good performance.
In this paper, we are committed to the study of generalized difference gap (D-gap) functions and error bounds for hemivariational inequalities in Hilbert spaces. By introducing a new gap function, we define a generali...
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In this paper, we are committed to the study of generalized difference gap (D-gap) functions and error bounds for hemivariational inequalities in Hilbert spaces. By introducing a new gap function, we define a generalized D-gap function for the hemivariational inequality considered, for which we investigate the local Lipschitz continuity and coercivity. Then, some error bound results for the generalized D-gap function are established and the relationship between the solution to the hemivariational inequality and the stationary point of the generalized D-gap function is discussed. Finally, we construct a descent algorithm for solving the hemivariational inequality based on the generalized D-gap function and further prove a convergence result for the algorithm.
Unplanned en-route charging of electric vehicles (EVs) can unexpectedly cripple traffic conditions. As lesseffective location of fast charging station (FCS) may exacerbate this issue, the effects of FCS on EVs' ch...
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Unplanned en-route charging of electric vehicles (EVs) can unexpectedly cripple traffic conditions. As lesseffective location of fast charging station (FCS) may exacerbate this issue, the effects of FCS on EVs' charging behaviors should be incorporated at the system planning stage. This paper proposes a strategic-chargingbehavior awared model in the context of electrified transportation network environment. This model is formulated into a bilevel mixed-integer programming problem. A newly designed network equilibrium model targets on the low-level problem, which is to model the drivers' charging reaction to a certain FCS layout. In considering the EV self-serving routing and charging behaviors as well as power network constraints, the upperlevel problem is formulated for location and sizing decision-makings, of which the objective is to minimize the overall traffic time and investment cost. To handle the proposed bilevel problem, a descent algorithm is further developed. To examine the effectiveness of the proposed approach, extensive numerical experiments are conducted, through which the obtained results demonstrate that the EV charging demand can perfectly be met while traffic congestions can be alleviated to a great extent.
A Nash-Cournot model for oligopolistic markets with concave cost functions and a differentiated commodity is analyzed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a...
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A Nash-Cournot model for oligopolistic markets with concave cost functions and a differentiated commodity is analyzed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity assumptions. The results of some numerical tests on randomly generated markets are also reported.
An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function...
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An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimate of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to guarantee that all the stationary points of a gap function actually solve QEP. A few classes of constraints satisfying such assumptions are identified covering a wide range of situations. Relying on these results, a descent method for solving QEP is devised and its convergence proved. Finally, error bounds are given in order to guarantee the boundedness of the sequence generated by the algorithm.
We consider a simplified model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identification procedure able to reconstruct the parameters of the model. The response of the mod...
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We consider a simplified model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identification procedure able to reconstruct the parameters of the model. The response of the model is nonlinear with respect to its parameters and the reconstruction of the parameters is achieved by the introduction of a new vectorial descent stepsize, which improves the convergence of the Levenberg-Marquardt minimization algorithm. The new vectorial descent stepsize can have negative and positive entries of different sizes, which fundamentally differs from standard scalar descent stepsize. The new algorithm is proved to converge and to outperform the standard scalar descent strategy. We also propose algorithms for the initialization of the parameters needed by the reconstruction procedure, when no a priori knowledge is available.
The results of optimistic model and pessimistic model are always not efficient for practical application because they are two extreme possibilities for ill-posed bilevel programming problem. This paper presents a new ...
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ISBN:
(纸本)9780769550169
The results of optimistic model and pessimistic model are always not efficient for practical application because they are two extreme possibilities for ill-posed bilevel programming problem. This paper presents a new model by transferring Minmax model to a Maxmin model to solve above shortcoming. And we prove, by this transformation, a more practical value between the optimistic value and the pessimistic value can be achieved. Then, a new descent algorithm is developed to solve this new model by considering the satisfying degree of the lower level. Finally, an illustrated numerical example is demonstrated to show the proposed new model and algorithm are feasible and we can get a better result from all the iterated points by this Maxmin model than by the two extreme models.
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