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1.
In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming
problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary
global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions,
local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization
methods for quadratic integer programming problems are very efficient and stable. 相似文献
2.
Z. Y. Wu Y. J. Yang F. S. Bai M. Mammadov 《Journal of Optimization Theory and Applications》2011,151(2):241-259
The quadratic knapsack problem (QKP) maximizes a quadratic objective function subject to a binary and linear capacity constraint. Due to its simple structure
and challenging difficulty, it has been studied intensively during the last two decades. This paper first presents some global
optimality conditions for (QKP), which include necessary conditions and sufficient conditions. Then a local optimization method for (QKP) is developed using the necessary global optimality condition. Finally a global optimization method for (QKP) is proposed based on the sufficient global optimality condition, the local optimization method and an auxiliary function.
Several numerical examples are given to illustrate the efficiency of the presented optimization methods. 相似文献
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4.
In this paper, a new local optimization method for mixed integer quadratic programming problems with box constraints is presented by using its necessary global optimality conditions. Then a new global optimization method by combining its sufficient global optimality conditions and an auxiliary function is proposed. Some numerical examples are also presented to show that the proposed optimization methods for mixed integer quadratic programming problems with box constraints are very efficient and stable. 相似文献
5.
Z. Y. Wu J. Quan G. Q. Li J. Tian 《Journal of Optimization Theory and Applications》2012,153(2):408-435
Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot
of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global
optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization
methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization
methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local
optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial
optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical
examples are also given to illustrate that these approaches are very efficient. 相似文献
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7.
《European Journal of Operational Research》2004,158(2):409-417
In this paper, general linear complementarity problems (LCPs) are studied via global optimization problems. In particular, unsolvable LCPs are reformulated as multicriteria optimization, minimax optimization and quadratic programming problems. The solvability and unsolvability of LCPs are obtained via these reformulations. Furthermore, first-order and second-order global optimality conditions of LCPs are derived. Some examples are also given to demonstrate these optimality conditions. 相似文献
8.
G. Danninger 《Journal of Optimization Theory and Applications》1992,75(3):535-558
Second-order necessary and sufficient conditions for local optimality in constrained optimization problems are discussed. For global optimality, a criterion recently developed by Hiriart-Urruty and Lemarechal is thoroughly examined in the case of concave quadratic problems and reformulated into copositivity conditions. 相似文献
9.
JinRong Wang Xuezhu Li Wei Wei 《Communications in Nonlinear Science & Numerical Simulation》2012,17(11):4384-4394
This paper is motivated from some recent papers treating the impulsive Cauchy problems for some differential equations with fractional order q ∈ (1, 2). A better definition of solution for impulsive fractional differential equation is given. We build up an effective way to find natural solution for such problems. Then sufficient conditions for existence of the solutions are established by applying fixed point methods. Four examples are given to illustrate the results. 相似文献
10.
In this paper, we present Lagrange multiplier necessary conditions for global optimality that apply to non-convex optimization
problems beyond quadratic optimization problems subject to a single quadratic constraint. In particular, we show that our
optimality conditions apply to problems where the objective function is the difference of quadratic and convex functions over
a quadratic constraint, and to certain class of fractional programming problems. Our necessary conditions become necessary
and sufficient conditions for global optimality for quadratic minimization subject to quadratic constraint. As an application,
we also obtain global optimality conditions for a class of trust-region problems. Our approach makes use of outer-estimators,
and the powerful S-lemma which has played key role in control theory and semidefinite optimization. We discuss numerical examples
to illustrate the significance of our optimality conditions.
The authors are grateful to the referees for their useful comments which have contributed to the final preparation of the
paper. 相似文献
11.
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions 总被引:3,自引:0,他引:3
In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange
multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization
problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange
multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least squares
with ellipsoidal constraints, and quadratic minimization with binary constraints. We discuss examples which demonstrate that
our optimality conditions can effectively be used for identifying global minimizers of certain multi-extremal non-convex quadratic
optimization problems.
The work of Z. Y. Wu was carried out while the author was at the Department of Applied Mathematics, University of New South
Wales, Sydney, Australia. 相似文献
12.
Z. Y. Wu 《Journal of Global Optimization》2007,39(3):427-440
In this paper, we present sufficient global optimality conditions for weakly convex minimization problems using abstract convex
analysis theory. By introducing (L,X)-subdifferentials of weakly convex functions using a class of quadratic functions, we first obtain some sufficient conditions
for global optimization problems with weakly convex objective functions and weakly convex inequality and equality constraints.
Some sufficient optimality conditions for problems with additional box constraints and bivalent constraints are then derived.
相似文献
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14.
A novel mathematical modeling of multiple scales (NMMMS) is presented for a class of singular perturbed problems with both boundary or transition layers in two dimensions. The original problems are converted into a series of problems with different scales, and under these different scales, each of the problem is regular. The rational spectral collocation method (RSCM) is applied to deal with the problems without singularities. NMMMS can still work successfully even when the parameter ε is extremely small (ε = 10?25 or even smaller). A brief error estimate for the model problem is given in Section 2. Numerical examples are implemented to show the method is of high accuracy and efficiency. 相似文献
15.
We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish
tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints,
such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality
conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract
convexity. 相似文献
16.
《Chaos, solitons, and fractals》2006,27(5):1317-1335
This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. By employing the detection function method for global bifurcations of limit cycles and the normal form theory for local degenerate Hopf bifurcations, 31 and 35 limit cycles and their configurations are obtained for different sets of controlled parameters. It is shown that: H(6) ⩾ 35 = 62 − 1, where H(6) is the Hilbert number for sixth-degree polynomial systems. 相似文献
17.
Guoyin Li 《Journal of Optimization Theory and Applications》2012,152(3):710-726
In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent
constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems
with quadratic equality and bivalent constraints. Then we examine situations where this optimality condition is equivalent
to checking the positive semidefiniteness of a related matrix, and so, can be verified in polynomial time by using elementary
eigenvalues decomposition techniques. As a consequence, we also present simple sufficient global optimality conditions, which
can be verified by solving a linear matrix inequality problem, extending several known sufficient optimality conditions in
the existing literature. 相似文献
18.
Andreas Lundell Joakim Westerlund Tapio Westerlund 《Journal of Global Optimization》2009,43(2-3):391-405
In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, often not all variables need to be transformed. A method for minimizing the number of original variables involved in the transformations is, therefore, presented. In order to illustrate how the given method can be integrated into the transformation framework, some mixed integer optimization problems including signomial functions are finally solved to global optimality using the given techniques. 相似文献
19.
Ivo Nowak 《Journal of Global Optimization》2000,18(4):337-356
A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap. 相似文献
20.
Stabilized sequential quadratic programming (sSQP) methods for nonlinear optimization generate a sequence of iterates with fast local convergence regardless of whether or not the active-constraint gradients are linearly dependent. This paper concerns the local convergence analysis of an sSQP method that uses a line search with a primal-dual augmented Lagrangian merit function to enforce global convergence. The method is provably well-defined and is based on solving a strictly convex quadratic programming subproblem at each iteration. It is shown that the method has superlinear local convergence under assumptions that are no stronger than those required by conventional stabilized SQP methods. The fast local convergence is obtained by allowing a small relaxation of the optimality conditions for the quadratic programming subproblem in the neighborhood of a solution. In the limit, the line search selects the unit step length, which implies that the method does not suffer from the Maratos effect. The analysis indicates that the method has the same strong first- and second-order global convergence properties that have been established for augmented Lagrangian methods, yet is able to transition seamlessly to sSQP with fast local convergence in the neighborhood of a solution. Numerical results on some degenerate problems are reported. 相似文献