共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of -subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas' lemma is obtained for inequality systems involving convex functions and is used to establish necessary and sufficient optimality conditions. As applications, optimality conditions are also given for weakly convex programming problems, convex maximization problems and for fractional programming problems.This paper was presented at the Optimization Miniconference held at the University of Ballarat, Victoria, Australia, on July 14, 1994. 相似文献
3.
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
4.
In this paper, we present necessary as well as sufficient conditions for a given feasible point to be a global minimizer of
the difference of quadratic and convex functions subject to bounds on the variables. We show that the necessary conditions
become necessary and sufficient for global minimizers in the case of a weighted sum of squares minimization problems. We obtain
sufficient conditions for global optimality by first constructing quadratic underestimators and then by characterizing global
minimizers of the underestimators. We also derive global optimality conditions for the minimization of the difference of quadratic
and convex functions over binary constraints. We discuss several numerical examples to illustrate the significance of the
optimality conditions.
The authors are grateful to the referees for their helpful comments and valuable suggestions which have contributed to the
final preparation of the paper. 相似文献
5.
In this paper, we develop necessary conditions for global optimality that apply to non-linear programming problems with polynomial
constraints which cover a broad range of optimization problems that arise in applications of continuous as well as discrete
optimization. In particular, we show that our optimality conditions readily apply to problems where the objective function
is the difference of polynomial and convex functions over polynomial constraints, and to classes of fractional programming
problems. Our necessary conditions become also sufficient for global optimality for polynomial programming problems. Our approach
makes use of polynomial over-estimators and, a polynomial version of a theorem of the alternative which is a variant of the
Positivstellensatz in semi-algebraic geometry. We discuss numerical examples to illustrate the significance of our optimality
conditions. 相似文献
6.
We consider convex problems of semi-infinite programming (SIP) using an approach based on the implicit optimality criterion.
This criterion allows one to replace optimality conditions for a feasible solution x
0 of the convex SIP problem by such conditions for x
0 in some nonlinear programming (NLP) problem denoted by NLP(I(x
0)). This nonlinear problem, constructed on the base of special characteristics of the original SIP problem, so-called immobile indices and their immobility orders, has a special structure and a diversity of important properties. We study these properties and use them to obtain efficient
explicit optimality conditions for the problem NLP(I(x
0)). Application of these conditions, together with the implicit optimality criterion, gives new efficient optimality conditions
for convex SIP problems. Special attention is paid to SIP problems whose constraints do not satisfy the Slater condition and
to problems with analytic constraint functions for which we obtain optimality conditions in the form of a criterion. Comparison
with some known optimality conditions for convex SIP is provided. 相似文献
7.
《Optimization》2012,61(6):627-639
Abstract: In this article, we consider the concave quadratic programming problem which is known to be NP hard. Based on the improved global optimality conditions by [Dür, M., Horst, R. and Locatelli, M., 1998, Necessary and sufficient global optimality conditions for convex maximization revisited, Journal of Mathematical Analysis and Applications, 217, 637–649] and [Hiriart-Urruty, J.B. and Ledyav, J.S., 1996, A note in the characterization of the global maxima of a convex function over a convex set, Journal of Convex Analysis, 3, 55–61], we develop a new approach for solving concave quadratic programming problems. The main idea of the algorithms is to generate a sequence of local minimizers either ending at a global optimal solution or at an approximate global optimal solution within a finite number of iterations. At each iteration of the algorithms we solve a number of linear programming problems with the same constraints of the original problem. We also present the convergence properties of the proposed algorithms under some conditions. The efficiency of the algorithms has been demonstrated with some numerical examples. 相似文献
8.
In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems with box as well as bivalent constraints. Our necessary optimality conditions can be numerically checked by solving semi-definite programming problems. Then, by employing separable polynomial under-estimators, we establish sufficient conditions for global optimality for classes of polynomial optimization problems with box or bivalent constraints. We construct underestimators using the sum of squares convex (SOS-convex) polynomials of real algebraic geometry. An important feature of SOS-convexity that is generally not shared by the standard convexity is that whether a polynomial is SOS-convex or not can be checked by solving a semidefinite programming problem. We illustrate the versatility of our optimality conditions by simple numerical examples. 相似文献
9.
《Optimization》2012,61(8):981-993
By using the concepts of local cone approximations and K-directional derivatives, we obtain necessary conditions of optimality for the weak efficiency of the vectorial optimization problems with the inequalities and abstract constraints. We introduce the notion of stationary point (weak and strong) and we prove that, under suitable hypotheses of K-invexity, the stationary points are weakly efficient solutions (global). 相似文献
10.
This paper provides characterizations of the weakly minimal elements of vector optimization problems and the global minima of scalar optimization problems posed on locally convex spaces whose objective functions are deterministic while the uncertain constraints are treated under the robust (or risk-averse) approach, i.e. requiring the feasibility of the decisions to be taken for any possible scenario. To get these optimality conditions we provide Farkas-type results characterizing the inclusion of the robust feasible set into the solution set of some system involving the objective function and possibly uncertain parameters. In the particular case of scalar convex optimization problems, we characterize the optimality conditions in terms of the convexity and closedness of an associated set regarding a suitable point. 相似文献
11.
Vsevolod I. Ivanov 《Journal of Mathematical Analysis and Applications》2009,356(1):30-41
In this paper we obtain first and second-order optimality conditions for an isolated minimum of order two for the problem with inequality constraints and a set constraint. First-order sufficient conditions are derived in terms of generalized convex functions. In the necessary conditions we suppose that the data are continuously differentiable. A notion of strongly KT invex inequality constrained problem is introduced. It is shown that each Kuhn-Tucker point is an isolated global minimizer of order two if and only if the problem is strongly KT invex. The article could be considered as a continuation of [I. Ginchev, V.I. Ivanov, Second-order optimality conditions for problems with C1 data, J. Math. Anal. Appl. 340 (2008) 646-657]. 相似文献
12.
In the present work, we intend to derive conditions characterizing globally optimal solutions of quadratic 0-1 programming
problems. By specializing the problem of maximizing a convex quadratic function under linear constraints, we find explicit
global optimality conditions for quadratic 0-1 programming problems, including necessary and sufficient conditions and some
necessary conditions. We also present some global optimality conditions for the problem of minimization of half-products. 相似文献
13.
Nazih Abderrazzak Gadhi Stephan Dempe 《Numerical Functional Analysis & Optimization》2013,34(15):1622-1634
AbstractThe paper is devoted to the study of a bilevel multiobjective optimization problems with objectives and constraints given as differences of convex functions. The main attention is paid to deriving sufficient optimality conditions. Several intermediate optimization problems are introduced to help us in our investigation. 相似文献
14.
Helmut Dietrich 《Journal of Global Optimization》1994,5(4):359-370
By means of suitable dual problems to the following global optimization problems: extremum{f(x): x M X}, wheref is a proper convex and lower-semicontinuous function andM a nonempty, arbitrary subset of a reflexive Banach spaceX, we derive necessary and sufficient optimality conditions for a global minimizer. The method is also applicable to other nonconvex problems and leads to at least necessary global optimality conditions. 相似文献
15.
X. Q. Yang 《Journal of Global Optimization》2004,30(2-3):271-284
Second-order optimality conditions are studied for the constrained optimization problem where the objective function and the constraints are compositions of convex functions and twice strictly differentiable functions. A second-order sufficient condition of a global minimizer is obtained by introducing a generalized representation condition. Second-order minimizer characterizations for a convex program and a linear fractional program are derived using the generalized representation condition 相似文献
16.
X. Q. Yang 《Journal of Global Optimization》2004,30(2):271-284
Second-order optimality conditions are studied for the constrained optimization problem where the objective function and the constraints are compositions of convex functions and twice strictly differentiable functions. A second-order sufficient condition of a global minimizer is obtained by introducing a generalized representation condition. Second-order minimizer characterizations for a convex program and a linear fractional program are derived using the generalized representation condition 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.
Tadeusz ANTCZAK 《数学物理学报(B辑英文版)》2017,37(4):1133-1150
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex. 相似文献
19.
Ivan Ginchev 《Journal of Global Optimization》2009,44(1):111-130
Let X be a real linear space, a convex set, Y and Z topological real linear spaces. The constrained optimization problem min
C
f(x), is considered, where f : X
0→ Y and g : X
0→ Z are given (nonsmooth) functions, and and are closed convex cones. The weakly efficient solutions (w-minimizers) of this problem are investigated. When g obeys quasiconvex properties, first-order necessary and first-order sufficient optimality conditions in terms of Dini directional
derivatives are obtained. In the special case of problems with pseudoconvex data it is shown that these conditions characterize
the global w-minimizers and generalize known results from convex vector programming. The obtained results are applied to the special case
of problems with finite dimensional image spaces and ordering cones the positive orthants, in particular to scalar problems
with quasiconvex constraints. It is shown, that the quasiconvexity of the constraints allows to formulate the optimality conditions
using the more simple single valued Dini derivatives instead of the set valued ones.
相似文献
20.
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