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21.
In this paper we study a system of linear operators between finite-dimensional Euclidean spaces. Emphasis is made on unbounded systems and sufficient conditions are established for their equi-surjectivity. An application is presented in which a system of approximate Jacobian matrices is used to obtain a parametric interior mapping theorem. A multiplier rule for vector problems is also derived. 相似文献
22.
Thomas Lorenz 《Set-Valued Analysis》2008,16(1):1-50
The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order
geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this
paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional
analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied
with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler
approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological
vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ
N
evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity
assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions
for the uniqueness of these solutions.
相似文献
23.
We have previously shown, by redundant Klee–Minty constructions, that the central path may arbitrarily closely visit every vertex of the Klee–Minty cube. In those constructions, the redundant constraints are far away from the feasible region. In this paper, we provide a construction in which all redundant constraints touch the feasible region. 相似文献
24.
Infinite-dimensional parameter-dependent optimization problems of the form ‘minJ(u;p) subject to g(u)?0’ are studied, where u is sought in an L∞ function space, J is a quadratic objective functional, and g represents pointwise linear constraints. This setting covers in particular control constrained optimal control problems. Sensitivities with respect to the parameter p of both, optimal solutions of the original problem, and of its approximation by the classical primal-dual interior point approach are considered. The convergence of the latter to the former is shown as the homotopy parameter μ goes to zero, and error bounds in various Lq norms are derived. Several numerical examples illustrate the results. 相似文献
25.
“语意学”在上世纪80年代在西方被引入设计领域。其创始人克里本多夫从广义上定义了设计中语意学的研究内容:设计作品不仅仅要具备物理功能,还要能够提示如何使用,具有象征功能,构成人们生活的象征环境。语意学在室内设计中承担了探求作品“潜台词”的作用,以更加明确的视觉形象和更具有象征意义的形态设计,传达给使用者更多的文化内涵,使室内设计作品更加适应人的生活习惯和心理感受,以提升设计的人性化品质。 相似文献
26.
Experimental studies were carried out to investigate projectile acceleration in a single-stage gun at breech pressures below
50 MPa. The gun was driven by firing either liquid or solid propellant. In-bore projectile velocity was continuously recorded
using the well-known, precise VISAR interferometer technique so that accurate projectile acceleration data could be deduced.
Both the attained projectile acceleration and muzzle exit velocity depend upon the charge-to-mass ratio and the pressure at
which the blow-out disk ruptures. The results obtained from these experiments render information on the interplay between
propellant combustion and projectile acceleration for low in-bore pressure regimes, and they provide the input data required
for adequate numerical simulation. 相似文献
27.
Trust region affine scaling algorithms for linearly constrained convex and concave programs 总被引:4,自引:0,他引:4
We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequence generated by the algorithm satisfies the first order necessary condition for optimality of the problem. For a special class of convex or concave functions satisfying a certain invariance condition on their Hessians, it is shown that the sequences of iterates and objective function values generated by the algorithm convergeR-linearly andQ-linearly, respectively. Moreover, under primal nondegeneracy and for this class of objective functions, it is shown that the limit point of the sequence of iterates satisfies the first and second order necessary conditions for optimality of the problem. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.The work of these authors was based on research supported by the National Science Foundation under grant INT-9600343 and the Office of Naval Research under grants N00014-93-1-0234 and N00014-94-1-0340. 相似文献
28.
Silvia Bonettini Emanuele Galligani Valeria Ruggiero 《Computational Optimization and Applications》2007,37(1):1-34
This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior
point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative
solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current
outer iterate is far from the solution.
In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior
point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical
experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison
with other interior point codes is also reported.
This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project:
“Parallel Nonlinear Numerical Optimization PN
2
O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ). 相似文献
29.
A. Nemirovski 《Mathematical Programming》1997,77(1):191-224
We develop a long-step surface-following version of the method of analytic centers for the fractional-linear problem min{t
0 |t
0
B(x) −A(x) εH, B(x) εK, x εG}, whereH is a closed convex domain,K is a convex cone contained in the recessive cone ofH, G is a convex domain andB(·),A(·) are affine mappings. Tracing a two-dimensional surface of analytic centers rather than the usual path of centers allows
to skip the initial “centering” phase of the path-following scheme. The proposed long-step policy of tracing the surface fits
the best known overall polynomial-time complexity bounds for the method and, at the same time, seems to be more attractive
computationally than the short-step policy, which was previously the only one giving good complexity bounds.
The research was partly supported by the Israeli-American Binational Science Foundation (BSF). 相似文献
30.
This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity
problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled
Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine
scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite
number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen
et al., SIAM Journal on Optimization 7 (1997) 126–140.
Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education,
Science and Culture, Japan.
Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028 相似文献