共查询到20条相似文献,搜索用时 218 毫秒
1.
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
2.
A. V. Arutyunov D. Yu. Karamzin 《Computational Mathematics and Mathematical Physics》2007,47(3):349-360
The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. 相似文献
3.
A. V. Arutyunov D. Yu. Karamzin 《Computational Mathematics and Mathematical Physics》2006,46(8):1293-1298
An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary conditions for this problem are given that strengthen previously known results. 相似文献
4.
A. V. Arutyunov 《Differential Equations》2009,45(11):1595-1601
We consider a quadratic optimal control problem on an infinite time interval with integral quadratic equality and inequality
constraints. For this (generally, nonconvex) problem, we justify the Lagrange constraint removal principle and the duality
relation. The obtained result is based on the general theory of extremal problems, namely, on necessary second-order extremum
conditions. 相似文献
5.
Journal of Optimization Theory and Applications - Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming... 相似文献
6.
G. V. Smirnov 《Journal of Optimization Theory and Applications》1996,88(3):671-688
We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints. 相似文献
7.
8.
An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7). 相似文献
9.
《Optimization》2012,61(2):353-399
Abstract Both parametric and parameter-free stationary-point-type and saddle-point-type necessary and sufficient optimality conditions are established for a class of nonsmooth continuous-time generalized fractional programming problems with Volterra-type integral inequality and nonnegativity constraints. These optimality criteria are then utilized for constructing ten parametric and parameter-free Wolfe-type and Lagrangian-type dual problems and for proving weak, strong, and strict converse duality theorems. Furthermore, it is briefly pointed out how similar optimality and duality results can be obtained for two important special cases of the main problem containing arbitrary norms and square roots of positive semidefinite quadratic forms. All the results developed here are also applicable to continuous-time programming problems with fractional, discrete max, and conventional objective functions, which are special cases of the main problem studied in this paper. 相似文献
10.
Mihai Popescu 《PAMM》2008,8(1):10899-10900
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrices, function of the state variable. Dynamic constraints are represented by a bilinear differential systems of the form. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, respectively the adjoint system corresponding to those functions. Thus it will be obtained a matrix differential equation where the solution representing the positive defined symmetric matrix P ( x ), verifies the Riccati algebraic equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
P.Q. KhanhN.D. Tuan 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4338-4351
Second-order necessary conditions and sufficient conditions for optimality in nonsmooth vector optimization problems with inclusion constraints are established. We use approximations as generalized derivatives and avoid even continuity assumptions. Convexity conditions are not imposed explicitly. Not all approximations in use are required to be bounded. The results improve or include several recent existing ones. Examples are provided to show that our theorems are easily applied in situations where several known results do not work. 相似文献
12.
K. Malanowski H. Maurer S. Pickenhain 《Journal of Optimization Theory and Applications》2004,123(3):595-617
Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints. 相似文献
13.
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
14.
Joseph Frédéric Bonnans Constanza Sánchez Fernández de la Vega 《Set-Valued and Variational Analysis》2010,18(3-4):307-326
We consider the optimal control problem of a class of integral equations with initial and final state constraints, as well as running state constraints. We prove Pontryagin’s principle, and study the continuity of the optimal control and of the measure associated with first order state constraints. We also establish the Lipschitz continuity of these two functions of time for problems with only first order state constraints. 相似文献
15.
Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications 总被引:1,自引:0,他引:1
In this paper, vector variational inequalities (VVI) with matrix inequality constraints are investigated by using the image
space analysis. Linear separation for VVI with matrix inequality constraints is characterized by using the saddle-point conditions
of the Lagrangian function. Lagrangian-type necessary and sufficient optimality conditions for VVI with matrix inequality
constraints are derived by utilizing the separation theorem. Gap functions for VVI with matrix inequality constraints and
weak sharp minimum property for the solutions set of VVI with matrix inequality constraints are also considered. The results
obtained above are applied to investigate the Lagrangian-type necessary and sufficient optimality conditions for vector linear
semidefinite programming problems as well as VVI with convex quadratic inequality constraints. 相似文献
16.
G. J. Zalmai 《Journal of Optimization Theory and Applications》1996,90(2):435-456
We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions. 相似文献
17.
Xiaoqi Yang 《Numerical Functional Analysis & Optimization》2013,34(5-6):621-632
Second-order necessary conditions for inequality and equality constrained C1, 1 optimization problems are derived. A constraint qualification condition which uses the recent generalized second-order directional derivative is employed to obtain these conditions. Various second-order sufficient conditions are given under appropriate conditions on the generalized second-order directional derivative in a neighborhood of a given point. An application of the secondorder conditions to a new class of nonsmooth C1, 1 optimization problems with infinitely many constraints is presented. 相似文献
18.
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
19.
F. J. Silva 《Set-Valued and Variational Analysis》2016,24(1):57-81
We consider the optimal control of a semilinear parabolic equation with pointwise bound constraints on the control and finitely many integral constraints on the final state. Using the standard Robinson’s constraint qualification, we provide a second order necessary condition over a set of strictly critical directions. The main feature of this result is that the qualification condition needed for the second order analysis is the same as for classical finite-dimensional problems and does not imply the uniqueness of the Lagrange multiplier. We establish also a second order sufficient optimality condition which implies, for problems with a quadratic Hamiltonian, the equivalence between solutions satisfying the quadratic growth property in the L 1 and \(L^{\infty }\) topologies. 相似文献
20.
We study optimal control problems for hyperbolic equations
(focusing on the multidimensional wave equation) with control functions in the Dirichlet
boundary conditions under hard/pointwise control and state constraints. Imposing
appropriate convexity assumptions on the cost integral functional, we establish the
existence of optimal control and derive new necessary optimality conditions in the
integral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems. 相似文献