Second-Order Karush-Kuhn-Tucker Optimality Conditions for Vector Problems with Continuously Differentiable Data and Second-Order Constraint Qualifications [PDF]
, 2014 Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with C$\sp{1}$ data, J.
Ivanov, Vsevolod I.
core +1 more source
Characterizations of the Solution Sets of Generalized Convex Fuzzy Optimization Problem
Open Mathematics, 2019 This paper provides some new characterizations of the solution sets for non-differentiable generalized convex fuzzy optimization problem. Firstly, we introduce some new generalized convex fuzzy functions and discuss the relationships among them. Secondly,
Chen Wang, Zhou Zhiang
doaj +1 more source
Global Solutions to Nonconvex Optimization of 4th-Order Polynomial and Log-Sum-Exp Functions [PDF]
, 2014 This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences.
Chen, Yi, Gao, David Y
core +1 more source
Strict global minimizers and higher-order generalized strong invexity in multiobjective optimization
Journal of Inequalities and Applications, 2013 Higher-order strict minimizers with respect to a nonlinear function for a multiobjective optimization problem are introduced and are characterized via sufficient optimality conditions and higher-order mixed saddle points of a vector-valued partial ...
Guneet Bhatia, Rishi Rajan Sahay
semanticscholar +2 more sources
Adaptive inexact fast augmented Lagrangian methods for constrained convex optimization [PDF]
, 2015 In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in [15] and the ...
Necoara, Ion +2 more
core +3 more sources
Optimality and duality in set-valued optimization utilizing limit sets
Open Mathematics, 2018 This paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality ...
Kong Xiangyu, Zhang Yinfeng, Yu GuoLin
doaj +1 more source
Symmetric duality for a class of multiobjective programming
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 9, Page 617-625, 2000., 2000 We formulate a pair of symmetric dual nondifferentiable multiobjective programming and establish appropriate duality theorems. We also show that differentiable and nondifferentiable analogues of several pairs of symmetric dual problems can be obtained as special cases of our general symmetric programs.
Xinmin Yang, Shouyang Wang, Duan Li
wiley +1 more source
Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces
Open Mathematics, 2019 A new class of generalized convex set-valued maps termed relatively solid generalized cone-subconvexlike maps is introduced in real linear spaces not equipped with any topology.
Liang Hongwei, Wan Zhongping
doaj +1 more source
On the connection of facially exposed and nice cones [PDF]
, 2012 A closed convex cone K is called nice, if the set K^* + F^\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\perp is the orthogonal complement of the linear span of F.
Pataki, Gabor
core +3 more sources
Least-Squares Covariance Matrix Adjustment [PDF]
, 2005 We consider the problem of finding the smallest adjustment to a given symmetric $n \times n$ matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive ...
Boyd, Stephen, Xiao, Lin
core +1 more source