共查询到20条相似文献,搜索用时 9 毫秒
1.
We formulate convex semi-infinite programming problems in a functional analytic setting and derive optimality conditions and several duality results, based on which we develop a computational framework for solving convex semi-infinite programs. 相似文献
2.
In this article, we study the generalized Levitin-Polyak well-posedness of generalized semi-infinite programs. We first give the criteria and characterizations for two types of well-posedness. We then establish the convergence of a class of penalty methods under the assumption of generalized type I Levitin-Polyak well-posedness. 相似文献
3.
Generalized semi-infinite optimization problems (GSIP) are considered. We generalize the well-known optimality conditions for minimizers of order one in standard semi-infinite programming to the GSIP case. We give necessary and sufficient conditions for local minimizers of order one without the assumption of local reduction. The necessary conditions are derived along the same lines as the first-order necessary conditions for GSIP in a recent paper of Jongen, Rückmann, and Stein (Ref. 1) by assuming the so-called extended Mangasarian–Fromovitz constraint qualification. Using the ideas of a recent paper of Rückmann and Shapiro, we give short proofs of necessary and sufficient optimality conditions for minimizers of order one under the additional assumption of the Mangasarian–Fromovitz constraint qualification at all local minimizers of the so-called lower-level problem. 相似文献
4.
C. Ling L. Q. Qi G. L. Zhou S. Y. Wu 《Journal of Optimization Theory and Applications》2006,129(1):147-164
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth
nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the
integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome
this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth
nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always
feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are
given.
Communicated by F. Giannessi
His work was supported by the Hong Kong Research Grant Council
His work was supported by the Australian Research Council. 相似文献
5.
In this article, we consider the convex min-max problem with infinite constraints. We propose an exchange method to solve the problem by using efficient inactive constraint dropping rules. There is no need to solve the maximization problem over the metric space, as the algorithm has merely to find some points in the metric space such that a certain criterion is satisfied at each iteration. Under some mild assumptions, the proposed algorithm is shown to terminate in a finite number of iterations and to provide an approximate solution to the original problem. Preliminary numerical results with the algorithm are promising. To our knowledge, this article is the first one conceived to apply explicit exchange methods for solving nonlinear semi-infinite convex min-max problems. 相似文献
6.
One of the major computational tasks of using the traditional cutting plane approach to solve linear semi-infinite programming problems lies in finding a global optimizer of a nonlinear and nonconvex program. This paper generalizes the Gustafson and Kortanek scheme to relax this requirement. In each iteration, the proposed method chooses a point at which the infinite constraints are violated to a degree, rather than a point at which the violations are maximized. A convergence proof of the proposed scheme is provided. Some computational results are included. An explicit algorithm which allows the unnecessary constraints to be dropped in each iteration is also introduced to reduce the size of computed programs. 相似文献
7.
Advances in Interval Methods for Deterministic Global Optimization in Chemical Engineering 总被引:2,自引:2,他引:0
In recent years, it has been shown that strategies based on an interval-Newton approach can be used to reliably solve a variety of nonlinear equation solving and optimization problems in chemical process engineering, including problems in parameter estimation and in the computation of phase behavior. These strategies provide a mathematical and computational guarantee either that all solutions have been located in an equation solving problem or that the global optimum has been found in an optimization problem. The primary drawback to this approach is the potentially high computational cost. In this paper, we consider strategies for bounding the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method. Recent preconditioning techniques for this purpose are reviewed, and a new bounding approach based on the use of linear programming (LP) techniques is presented. Using this approach it is possible to determine the desired bounds exactly (within round out), leading to significant overall improvements in computational efficiency. These techniques will be demonstrated using several global optimization problems, with focus on problems arising in chemical engineering, including parameter estimation and molecular modeling. These problems range in size from under ten variables to over two hundred, and are solved deterministically using the interval methodology. 相似文献
8.
9.
We study first-order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend
various well-known constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding
Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs takes
a weaker form unless a certain constraint qualification is satisfied. In the completely convex case where the objective of
the lower-level problem is concave and the constraint functions are quasiconvex, we show that the KKT condition takes a sharper
form.
The authors thank the anonymous referees for careful reading of the paper and helpful suggestions. The research of the first
author was partially supported by NSERC. 相似文献
10.
Abdelmalek Aboussoror 《Numerical Functional Analysis & Optimization》2014,35(7-9):816-836
This article deals with a generalized semi-infinite programming problem (S). Under appropriate assumptions, for such a problem we give necessary and sufficient optimality conditions via reverse convex problems. In particular, a necessary and sufficient optimality condition reduces the problem (S) to a min-max problem constrained with compact convex linked constraints. 相似文献
11.
在区间分析的基础上,对一类不等式约束的全局优化问题,给出几种新的不含全局极小的区域删除准则,提出了一个求不等式约束全局优化问题的区间算法.数值结果表明算法是可行和有效的. 相似文献
12.
一类非光滑总体极值的区间算法 总被引:1,自引:1,他引:0
本文利用区间分析知识 ,构造了一类 n维非光滑函数总体极值的区间算法 ,理论分析和实例计算均表明本文算法安全可靠 ;能求出全部总体极小点 ;收敛速度也比以前方法[1] 明显加快 相似文献
13.
14.
In this paper we define multisections of intervals that yield sharp lower bounds in branch-and-bound type methods for interval global optimization. A so called 'generalized kite', defined for differentiable univariate functions, is built simultaneously with linear boundary forms and suitably chosen centered forms. Proofs for existence and uniqueness of optimal cuts are given. The method described may be used either as an accelerating device or in a global optimization algorithm with an efficient pruning effect. A more general principle for decomposition of boxes is suggested. 相似文献
15.
16.
Using Interval Analysis for Solving Planar Single-Facility Location Problems: New Discarding Tests 总被引:3,自引:0,他引:3
Interval analysis is a powerful tool which allows the design of branch-and-bound methods able to solve many global optimization problems. The key to the speed of those methods is the use of several tests to discard boxes or parts of boxes in which no optimal point may occur. In this paper we present three new discarding tests for two-dimensional problems which are specially suitable for planar single-facility location problems. The usefulness of the new tests is shown by a computational study. 相似文献
17.
A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each
constraint in the problem formulation by a node of the DAG, with edges representing the flow of the computation. Using bounds
on ranges of intermediate results, represented as weights on the nodes and a suitable mix of forward and backward evaluation,
it is possible to give efficient implementations of interval evaluation and automatic differentiation. It is shown how to
combine this with constraint propagation techniques to produce narrower interval derivatives and slopes than those provided
by using only interval automatic differentiation preceded by constraint propagation. The implementation is based on earlier
work by L.V. Kolev, (1997), Reliable Comput., 3, 83–93 on optimal slopes and by C. Bliek, (1992), Computer Methods for Design Automation, PhD Thesis, Department of Ocean Engineering, Massachusetts Institute of Technology on backward slope evaluation. Care is
taken to ensure that rounding errors are treated correctly. Interval techniques are presented for computing from the DAG useful
redundant constraints, in particular linear underestimators for the objective function, a constraint, or a Lagrangian. The
linear underestimators can be found either by slope computations, or by recursive backward underestimation. For sufficiently
sparse problems the work is proportional to the number of operations in the calculation of the objective function (resp. the
Lagrangian).
Mathematics Subject Classification (2000). primary 65G40, secondary 90C26 相似文献
18.
A Cutting Plane Algorithm for Linear Reverse Convex Programs 总被引:1,自引:0,他引:1
In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problem arises in many applications such as engineering design, communications networks, and many management decision support systems with budget constraints and economies-of-scale. The main difficulty with this type of problem is the presence of the complicated reverse convex constraint, which destroys the convexity and possibly the connectivity of the feasible region, putting the problem in a class of difficult and mathematically intractable problems. We present a cutting plane method within the scope of a branch-and-bound scheme that efficiently partitions the polytope associated with the linear constraints and systematically fathoms these portions through the use of the bounds. An upper bound and a lower bound for the optimal value is found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed. 相似文献
19.
20.
Liu Y. Ito S. Lee H. W. J. Teo K. L. 《Journal of Optimization Theory and Applications》2001,108(3):617-632
Consider the class of linear-quadratic (LQ) optimal control problems with continuous linear state constraints, that is, constraints imposed on every instant of the time horizon. This class of problems is known to be difficult to solve numerically. In this paper, a computational method based on a semi-infinite programming approach is given. The LQ optimal control problem is formulated as a positive-quadratic infinite programming problem. This can be done by considering the control as the decision variable, while taking the state as a function of the control. After parametrizing the decision variable, an approximate quadratic semi-infinite programming problem is obtained. It is shown that, as we refine the parametrization, the solution sequence of the approximate problems converges to the solution of the infinite programming problem (hence, to the solution of the original optimal control problem). Numerically, the semi-infinite programming problems obtained above can be solved efficiently using an algorithm based on a dual parametrization method. 相似文献