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61.
J. B. G. Frenk J. Gromicho S. Zhang 《Journal of Optimization Theory and Applications》1996,89(1):65-87
This paper studies the problem of deciding whether the present iteration point of some algorithm applied to a planar singlefacility min-max location problem, with distances measured by either anl
p
-norm or a polyhedral gauge, is optimal or not. It turns out that this problem is equivalent to the decision problem of whether 0 belongs to the convex hull of either a finite number of points in the plane or a finite number of differentl
q
-circles
. Although both membership problems are theoretically solvable in polynomial time, the last problem is more difficult to solve in practice than the first one. Moreover, the second problem is solvable only in the weak sense, i.e., up to a predetermined accuracy. Unfortunately, these polynomial-time algorithms are not practical. Although this is a negative result, it is possible to construct an efficient and extremely simple linear-time algorithm to solve the first problem. Moreover, this paper describes an implementable procedure to reduce the second decision problem to the first with any desired precision. Finally, in the last section, some computational results for these algorithms are reported.The work of the second author was supported by JNICT (Portugal), under Contract BD/631/90-RM, during his stay at Erasmus University in Rotterdam.The authors would like to express their acknowledgments to Jan Brinkhuis for his suggestions and support and to Joe Mitchell for suggesting the simplifications leading to Algorithm 3.1. Also, the anonymous referees are acknowledged for their careful reading of the paper and their useful comments. 相似文献
62.
In this paper a basic structural problem in Generalized Semi-Infinite Programming is solved. In fact, under natural and generic
assumptions we show that at any (local) minimizer the “Symmetric Reduction Ansatz” holds.
相似文献
63.
64.
First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems 总被引:2,自引:0,他引:2
First-order and second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The necessary conditions are immediate generalizations of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as illustrated by a counterexample. Here, to go from finite to infinite dimensions, causes an essential change in the proof-techniques and the results. We present modified sufficient conditions of first-order and of second-order which are based on a strengthening of the usual assumptions on the derivative of the objective function and on the second derivative of the Lagrangian. 相似文献
65.
Jean-Paul Penot 《Mathematical Programming》1994,67(1-3):225-245
New second order optimality conditions for mathematical programming problems and for the minimization of composite functions are presented. They are derived from a general second order Fermat's rule for the minimization of a function over an arbitrary subset of a Banach space. The necessary conditions are more accurate than the recent results of Kawasaki (1988) and Cominetti (1989); but, more importantly, in the finite dimensional case they are twinned with sufficient conditions which differ by the replacement of an inequality by a strict inequality. We point out the equivalence of the mathematical programming problem with the problem of minimizing a composite function. Our conditions are especially important when one deals with functional constraints. When the cone defining the constraints is polyhedral we recover the classical conditions of Ben-Tal—Zowe (1982) and Cominetti (1990). 相似文献
66.
M. Hassan Farshbaf-Shaker 《Numerical Functional Analysis & Optimization》2013,34(11):1321-1349
A scalar Allen-Cahn-MPEC problem is considered and a penalization technique is applied to show the existence of an optimal control. We show that the stationary points of the penalized problems converge to some stationary points of the limit problem, which however are weaker than C-stationarity conditions. 相似文献
67.
Ben Liu 《Numerical Functional Analysis & Optimization》2013,34(1):50-67
In this article, we introduce a second-order modified contingent cone and a second-order modified contingent epiderivative. We discuss some properties of the second-order cone and the epiderivative, respectively. Moreover, a Fritz John type necessary optimality condition is obtained for the set-valued optimization problems with constraints by using the second-order modified contingent epiderivative and an example is proposed to explain the Fritz John type necessary optimality condition. In particular, we obtain a unified second-order sufficient and necessary optimality condition for the set-valued optimization problems with constraints under twice differentiable L-quasi-convex assumption. 相似文献
68.
In this article, we develop a numerical study of an optimal harvesting problem for age-dependent prey-predator system. Here, the rates of growth and decay as well as the interaction effect between species are assumed to be depending on age, time and space. Existence, uniqueness, and necessary conditions for the optimal control are assured in case of a small final time T. The discrete parabolic nonlinear dynamical systems are obtained by using a finite difference semi-implicit scheme. Then a numerical algorithm is developed to approximate the optimal harvesting effort and the optimal harvest. Results of the numerical tests are given. 相似文献
69.
Previous studies on thermal engine models and energy-converting biological systems have shown that some of the parameters affecting their thermodynamic performance also affect their dynamic stability. In some cases, such parameters represent a tradeoff between these two generic properties. In the present work we carry out a similar analysis on a simple model for an enzymatic reaction. Despite its simplicity, this model captures the essential characteristics of numerous biochemical reactions where an endothermic reaction is made possible by coupling it (via an enzyme) with an exothermic reaction. Our results indicate that the global reaction chemical potential gap () affects both the thermodynamic properties and stability of the steady state. Larger values imply a higher power output and a higher efficiency, but also a less strongly stable steady state. 相似文献
70.
Christian Clason Barbara Kaltenbacher Slobodan Veljovi? 《Journal of Mathematical Analysis and Applications》2009,356(2):738-751
This paper is concerned with optimal Neumann boundary control for the Westervelt and the Kuznetsov equations, which are equations of nonlinear acoustics. Specifically, functionals of tracking type with applications in noninvasive ultrasonic medical treatments are considered. Existence of optimal controls is established and first order necessary optimality conditions are derived. Stability of the minimizer with respect to perturbations in the data as well as convergence of the controls when the regularization parameter tends to zero is shown. 相似文献