[13] J.-E. Martınez-Legaz, On lower subdifferentiable functions, in Trends in ... [31] F. Plastria, Lower subdifferentiable functions and their minimization by cutting ...
IRREGULAR INEQUALITY-CONSTRAINED PROBLEMS. 1281 .... differentiable at a point ¯x, we mean that it is Fréchet-differentiable on a neighborhood.
of Exponential Smoothing Forecast Procedures. Johannes Ledolter* and George E.P. Box**. PREFACE. The use at time t of available observations from a time.
In this paper, a nonsmooth multiobjective programming problem is in- troduced and ... the objective and constraint functions are continuously differentiable. Later ...
Mar 16, 2014 - Shengkun Zhu1,2 and Shengjie Li2. 1 Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu ...
Jan 9, 2015 - OC] 9 Jan 2015 ... (Submitted Feb 5, 2014; Revised May 16, July 14 and Dec 16, 2014; Accepted Jan 8, 2015) ...... Appl. 2013;66:668â676.
(4.4). Due to assumed continuity of the constraint functions Ït(·) as t â T, they are subdifferentiable and satisfy the relation. Ï. â t (u) = ãu, yã â Ït(y) whenever u ...
May 23, 2016 - accurate recovery of hidden representation given the data when we forward ..... is the activation function and Ëx is a corrupted version of x.
Springer Science+Business Media, LLC 2012. Abstract The ... Department of Mathematics and Computer Science, TU Bergakademie Freiberg, Akademiestr. 6,.
Consider the nonlinear programming problem with polynomial constraints ... conditions that don't just provide necessary optimality conditions for nonlinear pro-.
Jan 1, 2013 - set functions and proved that the alternative theorem is valid for convex set ..... [8] H.-C. Lai and L.-J. Lin, âMoreau-Rockafellar type theorem for.
Mar 12, 2009 - mization problem with finite equalities and inequalities constraints: .... h is said to be Fréchet differentiable at ˆx if Dh(ˆx) ∈ L(X, Y ) and the ...
Dec 17, 2015 - Keywords: Nonlinear semidefinite programming, squared slack ... semidefinite matrices in Sm. Second-order optimality conditions for such ...
Programming Problems involving Generalized H-Derivative. I. Ahmada ... invex interval valued programming problems involving gH-differentiability. Moreover by ...
Jun 25, 2018 - †Department of Applied Mathematics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, 13083-859,. Campinas, SP, Brazil.
Dec 29, 2006 - mappings with generalized K subconvexlike derivatives. We consider ..... (x), x ∈ Ω, is called the Gateaux derivative of h at ¯x. Remark 4.1.
ki(x) = s(x|Ci), i = 1, 2, ··· , p. Then, ki is a convex function and. âki(x) = {w â Ci | ãw, xã = s(x|Ci)}, where âki is the subdifferentiable of ki (see [12]). Definition 2.1.
Feb 4, 2011 - [30] F. Plastria, Lower subdifferentiable functions and their minimization by cutting planes, Journal of Optimization Theory and Applications 46 ...
Key words. optimal control of partial differential equations, nondifferentiable objective, sparse controls, finite ... An answer to this question is given by solving the.
Mar 22, 2011 - linear and convex problems of infinite programming with inequality constraints. ... In this paper we focus on the so-called Fréchet/regular.
Dec 6, 2006 - duality theorems for differentiable fractional minimax programming. ... minimax programming problems in a Banach space; he established ...
since [Jf (x0),Jg(x0)] is equal to the identity matrix. ...... Report n.141- Proiezioni demografiche con algoritmi di consistenza per la popolazione .... 181 â Asset Prices under Bounded Rationality and Noise Trading (Emilio Barucci, Massimiliano.
[email protected]. Ville-Pekka Eronen. University of Turku, Department of Mathematics and Statistics. FI-20014 Turku, Finland [email protected]. Napsu Karmitsa.
The phrase convex optimization refers to the minimization of a convex function over a convex set. However the feasible convex set need not be always ...
Dec 9, 2006 - conditions for multi-objective programming can be found in [7], [13], [1],[4] and [3]. .... f : n â l be twice continuously differentiable around x.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
doi:10.3934/jimo.2017089
SECOND-ORDER OPTIMALITY CONDITIONS FOR CONE CONSTRAINED MULTI-OBJECTIVE OPTIMIZATION
Liwei Zhang∗ , Jihong Zhang and Yule Zhang School of Mathematical Sciences Dalian University of Technology Dalian 116024, China
(Communicated by Kok Lay Teo) Abstract. The aim of this paper is to develop second-order necessary and second-order sufficient optimality conditions for cone constrained multiobjective optimization. First of all, we derive, for an abstract constrained multi-objective optimization problem, two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions. Secondly, basing on the optimality results for the abstract problem, we demonstrate, for cone constrained multi-objective optimization problems, the first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as the second-order sufficient optimality conditions under upper second-order regularity for the conic constraint. Finally, using the optimality conditions for cone constrained multi-objective optimization obtained, we establish optimality conditions for polyhedral cone, second-order cone and semi-definite cone constrained multi-objective optimization problems.
1. Introduction. For and a and b in b
iff iff iff
ai ≥ bi , i = 1, . . . , l; a b, and a 6= b; ai > bi , i = 1, . . . , l.
