共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper a successive optimization method for solving inequality constrained optimization problems is introduced via a parametric monotone composition reformulation. The global optimal value of the original constrained optimization problem is shown to be the least root of the optimal value function of an auxiliary parametric optimization problem, thus can be found via a bisection method. The parametric optimization subproblem is formulated in such a way that it is a one-parameter problem and its value function is a monotone composition function with respect to the original objective function and the constraints. Various forms can be taken in the parametric optimization problem in accordance with a special structure of the original optimization problem, and in some cases, the parametric optimization problems are convex composite ones. Finally, the parametric monotone composite reformulation is applied to study local optimality. 相似文献
2.
《Optimization》2012,61(2):203-221
We propose an (α,β)-optimal solution concept of fuzzy optimization problem based on the possibility and necessity measures. It is well known that the set of all fuzzy numbers can be embedded into a Banach space isometrically and isomorphically. Inspired by this embedding theorem, we can transform the fuzzy optimization problem into a biobjective programming problem by applying the embedding function to the original fuzzy optimization problem. Then the (α,β)-optimal solutions of fuzzy optimization problem can be obtained by solving its corresponding biobjective programming problem. We also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed as fuzzy numbers). Under a setting of core value of fuzzy numbers, we provide the Karush–Kuhn–Tucker optimality conditions and show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also a (1,1)-optimal solution of the original fuzzy optimization problem. 相似文献
3.
We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a D.C. programming problem, thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via pth power transformation. We then prove that a class of nonconvex minimization problems can be always reduced to a monotone optimization problem, thus a concave minimization problem or a D.C. programming problem. 相似文献
4.
《Optimization》2012,61(4):627-643
Recently, the so-called second order cone optimization problem has received much attention, because the problem has many applications and the problem can in theory be solved efficiently by interior-point methods. In this note we treat duality for second order cone optimization problems and in particular whether a nonzero duality gap can be obtained when casting a convex quadratically constrained optimization problem as a second order cone optimization problem. Furthermore, we also discuss the p -order cone optimization problem which is a natural generalization of the second order case. Specifically, we suggest a new self-concordant barrier for the p -order cone optimization problem. 相似文献
5.
Jane J. Ye 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1642-1654
The exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem, and the reverse property is rarely studied. In this paper, we study the reverse property. We give the conditions under which the original constrained (single and/or multiobjective) optimization problem and the unconstrained exact penalized problem are exactly equivalent. The main conditions to ensure the exact penalty principle for optimization problems include the global and local error bound conditions. By using variational analysis, these conditions may be characterized by using generalized differentiation. 相似文献
6.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2006,5(4):331-353
Scalarization of the fuzzy optimization problems using the embedding theorem and the concept of convex cone (ordering cone)
is proposed in this paper. Two solution concepts are proposed by considering two convex cones. The set of all fuzzy numbers
can be embedded into a normed space. This motivation naturally inspires us to invoke the scalarization techniques in vector
optimization problems to solve the fuzzy optimization problems. By applying scalarization to the optimization problem with
fuzzy coefficients, we obtain its corresponding scalar optimization problem. Finally, we show that the optimal solution of
its corresponding scalar optimization problem is the optimal solution of the original fuzzy optimization problem. 相似文献
7.
8.
Jinghao Zhu Shangrui Zhao Guohua Liu 《Journal of Optimization Theory and Applications》2014,161(3):828-836
This paper presents a study on solutions to the global minimization of polynomials. The backward differential flow by the K–T equation with respect to the optimization problem is introduced to deal with a ball-constrained optimization problem. The unconstrained optimization is reduced to a constrained optimization problem which can be solved by a backward differential flow. Some examples are illustrated with an algorithm for computing the backward flow. 相似文献
9.
徐惠芳 《数学年刊A辑(中文版)》2011,32(2):141-160
对一类偏积分-微分方程中参数校准的反问题进行研究.在弱解的框架下,原问题可转化为含具体正则化项的最优化问题.文中证明了该最优化问题的解的存在性和稳定性,并考察了最优解存在的一阶必要条件.另外,证明了当正则化参数足够大时,该最优化问题关于参数a的凸性性质.基于偏积分-微分方程反问题的研究对于金融市场中的模型校准问题具有重要的意义. 相似文献
10.
11.
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems 总被引:23,自引:0,他引:23
Masao Fukushima 《Mathematical Programming》1992,53(1-3):99-110
Whether or not the general asymmetric variational inequality problem can be formulated as a differentiable optimization problem has been an open question. This paper gives an affirmative answer to this question. We provide a new optimization problem formulation of the variational inequality problem, and show that its objective function is continuously differentiable whenever the mapping involved in the latter problem is continuously differentiable. We also show that under appropriate assumptions on the latter mapping, any stationary point of the optimization problem is a global optimal solution, and hence solves the variational inequality problem. We discuss descent methods for solving the equivalent optimization problem and comment on systems of nonlinear equations and nonlinear complementarity problems. 相似文献
12.
《Optimization》2012,61(4):577-591
In this paper a problem of the linear Chebyshev approximation with respect to a vectorial norm in investigated. With the aid of abstract results of vector optimization a dual finite vector optimization problem will be assigned to this approximation problem. Further, an alternation theorem can be formulated. 相似文献
13.
In this paper, we present a new approach to solve a class of optimal discrete-valued control problems. This type of problem
is first transformed into an equivalent two-level optimization problem involving a combination of a discrete optimization
problem and a standard optimal control problem. The standard optimal control problem can be solved by existing optimal control
software packages such as MISER 3.2. For the discrete optimization problem, a discrete filled function method is developed
to solve it. A numerical example is solved to illustrate the efficiency of our method. 相似文献
14.
This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as a polynomial optimization problem by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization problem. We also prove that the assumption of nonsingularity in Nie’s method can be weakened to the finiteness of singularities. Some numerical examples are given in the end. 相似文献
15.
We consider the generalized Nash equilibrium problem which, in contrast to the standard Nash equilibrium problem, allows joint
constraints of all players involved in the game. Using a regularized Nikaido-Isoda-function, we then present three optimization
problems related to the generalized Nash equilibrium problem. The first optimization problem is a complete reformulation of
the generalized Nash game in the sense that the global minima are precisely the solutions of the game. However, this reformulation
is nonsmooth. We then modify this approach and obtain a smooth constrained optimization problem whose global minima correspond
to so-called normalized Nash equilibria. The third approach uses the difference of two regularized Nikaido-Isoda-functions
in order to get a smooth unconstrained optimization problem whose global minima are, once again, precisely the normalized
Nash equilibria. Conditions for stationary points to be global minima of the two smooth optimization problems are also given.
Some numerical results illustrate the behaviour of our approaches. 相似文献
16.
Nguyen V. Thoai 《Journal of Global Optimization》2012,52(3):499-508
Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function
program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global
optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we
propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By
the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential)
objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions.
Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can
be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria.
This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions
of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase
the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple
objective optimization. 相似文献
17.
《European Journal of Operational Research》1999,117(2):239-252
An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem. 相似文献
18.
We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers. 相似文献
19.
研究了多概率分布簇下的多损失下的WCVaR(Multi Worst Conditional Value-at-Risk)模型等价性定理, 根据概率分布簇的VaR测度值, 定义了多损失下的WCVaR风险测度值和对应的多目标优化模型(MWCVaR), 证明了多目标优化模型(MWCVaR)等价另一个多目标优化模型求解. 对于有限分布簇情形, 在一定条件下, 证明了用有限个分布簇就可以近似计算多损失(MWCVaR)优化模型. 相似文献