共查询到10条相似文献,搜索用时 31 毫秒
1.
Hang Nguyen T. V. Mordukhovich Boris S. Sarabi M. Ebrahim 《Mathematical Programming》2020,180(1-2):75-116
Mathematical Programming - The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream... 相似文献
2.
In aggregation for data envelopment analysis (DEA), a jointly measured efficiency score among inputs and outputs is desirable in performance analysis. A separate treatment between output-oriented efficiency and input-oriented efficiency is often needed in the conventional radial DEA models. Such radial measures usually need to measure both that a current performance attains an efficiency frontier and that all the slacks are zero on optimality. In the analytical framework of the radial measure, Russell measure is proposed to deal with such a difficulty. A major difficulty associated with the Russell measure is that it is modeled by a nonlinear programming formulation. Hence, a conventional linear programming algorithm, usually applied for DEA, cannot solve the Russell measure. This study newly proposes a reformulation of the Russell measure by a second-order cone programming (SOCP) model and applies the primal–dual interior point algorithm to solve the Russell measure. 相似文献
3.
T.R. Gulati S.K. Gupta I. Ahmad 《Journal of Computational and Applied Mathematics》2008,220(1-2):347-354
Wolfe and Mond–Weir type second-order symmetric duals are formulated and appropriate duality theorems are established under η-bonvexity/η-pseudobonvexity assumptions. This formulation removes several omissions in an earlier second-order primal dual pair introduced by Devi [Symmetric duality for nonlinear programming problems involving η-bonvex functions, European J. Oper. Res. 104 (1998) 615–621]. 相似文献
4.
In this paper, we formulate Wolfe and Mond–Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under η-bonvexity/η-pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric. 相似文献
5.
《Optimization》2012,61(5):489-503
We introduce a notion of a second-order invex function. A Fréchet differentiable invex function without any further assumptions is second-order invex. It is shown that the inverse claim does not hold. A Fréchet differentiable function is second-order invex if and only if each second-order stationary point is a global minimizer. Two complete characterizations of these functions are derived. It is proved that a quasiconvex function is second-order invex if and only if it is second-order pseudoconvex. Further, we study the nonlinear programming problem with inequality constraints whose objective function is second-order invex. We introduce a notion of second-order type I objective and constraint functions. This class of problems strictly includes the type I invex ones. Then we extend a lot of sufficient optimality conditions with generalized convex functions to problems with second-order type I invex objective function and constraints. Additional optimality results, which concern type I and second-order type I invex data are obtained. An answer to the question when a kernel, which is not identically equal to zero, exists is given. 相似文献
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We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound. 相似文献
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9.
A. Ben-Tal 《Journal of Optimization Theory and Applications》1980,31(2):143-165
This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.This research was partly supported by Project No. NR-947-021, ONR Contract No. N00014-75-0569, with the Center for Cybernetic Studies, and by the National Science Foundation, Grant No. NSF-ENG-76-10260. 相似文献
10.
Qinghong Zhang 《4OR: A Quarterly Journal of Operations Research》2011,9(4):403-416
It is known that the minimal cone for the constraint system of a conic linear programming problem is a key component in obtaining
strong duality without any constraint qualification. For problems in either primal or dual form, the minimal cone can be written
down explicitly in terms of the problem data. However, due to possible lack of closure, explicit expressions for the dual
cone of the minimal cone cannot be obtained in general. In the particular case of semidefinite programming, an explicit expression
for the dual cone of the minimal cone allows for a dual program of polynomial size that satisfies strong duality. In this
paper we develop a recursive procedure to obtain the minimal cone and its dual cone. In particular, for conic problems with
so-called nice cones, we obtain explicit expressions for the cones involved in the dual recursive procedure. As an example
of this approach, the well-known duals that satisfy strong duality for semidefinite programming problems are obtained. The
relation between this approach and a facial reduction algorithm is also discussed. 相似文献