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81.
Tim Hoheisel 《Journal of Mathematical Analysis and Applications》2008,337(1):292-310
We consider a class of optimization problems that is called a mathematical program with vanishing constraints (MPVC for short). This class has some similarities to mathematical programs with equilibrium constraints (MPECs for short), and typically violates standard constraint qualifications, hence the well-known Karush-Kuhn-Tucker conditions do not provide necessary optimality criteria. In order to obtain reasonable first order conditions under very weak assumptions, we introduce several MPVC-tailored constraint qualifications, discuss their relation, and prove an optimality condition which may be viewed as the counterpart of what is called M-stationarity in the MPEC-field. 相似文献
82.
In this paper, we establish existence theorems of quasivariational inclusion problems; from them, we establish existence theorems
of mathematical programs with quasivariational inclusion constraint, bilevel problems, mathematical programs with equilibrium
constraint and semi-infinite problems.
This research was supported by the National Science Council of the Republic of China. The authors express their gradtitude
to the referees for valuable suggestions. 相似文献
83.
讨论了交连续dcpo的遗传性和不变性,证明了如下结论:(1)交连续dcpo对于开子空间和闭子空间都是可遗传的;(2)交连续dcpo在加最大元和去最小元运算下保持交连续性;(3)交连续dcpo的收缩核为交连续dcpo.另外,给出了交连续的主理想刻画的一个直接证明;构造了反例说明交连续dcpo对于主滤子是不可遗传的;也构造了反例说明所有主滤子都交连续的一个dcpo,自身不必是交连续的. 相似文献
84.
M. Fampa L. A. Barroso D. Candal L. Simonetti 《Computational Optimization and Applications》2008,39(2):121-142
In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale
energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit
price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower
is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered
by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose
efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions
are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic
proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures
is illustrated in case studies with configurations derived from the Brazilian power system. 相似文献
85.
Hiroyoshi Mitake 《Applied Mathematics and Optimization》2008,58(3):393-410
We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general
convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary
condition to asymptotic solutions as time goes to infinity. 相似文献
86.
In this note, we obtain a sufficient and necessary condition for a point to be a local minimizer of a continuous optimization problem with maximin constraints via the local minimizers of its transformed standard nonlinear optimization problem. 相似文献
87.
The classical and quantum mechanics of a system of directly interacting relativistic particles is discussed. We first discuss
the spin-zero case, where we basically follow Rohrlich in introducing a set of covariant centre of mass (CM) and relative
variables. The relation of these to the classic formulation of Bakamjian and Thomas is also discussed. We also discuss the
important case of relativistic potentials which may depend on total four-momentum squared. We then consider the quantum mechanical
case of spin-half particles. The negative energy difficulty is solved by introducing a number of first class constraints which
fix the spinor structure of physical solutions and ensure the existence of proper CM and relative variables. We derive the
form of interactions consistent with Lorentz invariance, space inversion, time reversal and charge conjugation and with the
above mentioned first class constraints and find that it is analogous to that for the non-relativistic case. Finally the relationship
of the present work with some previous work is briefly discussed. 相似文献
88.
M. C. Bartholomew-Biggs 《Journal of Optimization Theory and Applications》1986,48(2):215-227
This report illustrates, by means of numerical examples, the behavior of the constrained minimization algorithm REQP in situations where the active constraint normals are not linearly independent. The examples are intended to demonstrate that the presence of the penalty parameter in the equations for calculating the Lagrange multiplier estimates enables a useful search direction to be computed. This is shown to be true, whether the dependence among the constraint normals occurs at the solution or in some other region. 相似文献
89.
N. G. van Kampen 《Journal of statistical physics》1986,44(1-2):1-24
The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due to a physical agency that forces the motion to remain on a manifold, or they represent conserved quantities of the equation of motion themselves. Also the Brownian motion is described either by a Smoluchowski diffusion equation or by a Kramers equation. The four cases lead to the following conclusions, (i) Smoluchowski diffusion with a conserved quantity reduces to a diffusion equation on the manifold; (ii) The same is true for diffusion with a physical constraint in three dimensions, but in more dimensions it may happen thatno autonomous equation on the manifold results; (iii) A Kramers equation with a conserved quantity reduces to an equation on the manifold, but in general not of the form of a Kramers equation; (iv) The Kramers equation with a physical constraint reduces to an autonomous Kramers equation on the manifold only for a special shape of that constraint. Throughout, only a certain type of physical constraints has been envisaged, and global questions are ignored. Finally, the customary heuristic construction of a Fokker-Planck equation for a mechanical system on a manifold is demonstrated for the case of Brownian rotation of a rigid body, and its shortcomings are emphasized. 相似文献
90.
Most writers on frequency assignment algorithms have described the details of a single algorithm, and evaluated the algorithm on selected data sets. There has been relatively little emphasis on describing the common features that are important if an algorithm is to have good performance. This paper describes the key features, with particular emphasis on algorithms for weighted fixed spectrum problems. The use of algorithms handling weighted constraints has become increasingly common in recent years. The advantages and disadvantages of weighting constraints are demonstrated. 相似文献