DUALITY AND ALTERNATIVE IN MULTIOBJECTTVE OPTIMIZATION ...
Recommend Documents
May 13, 2009 - (b) If for (PCC) and (DCC1 ) stable strong duality holds, then for all x â X ... dual problem, which can be seen as a refinement of (DCC1 ), ...
mization problems, namely, a convex multiobjective problem with cone inequality
constraints and a special fractional programming problem with linear inequality.
constraint satisfaction can be classified as inference duals, relaxation duals, or ... A constraint satisfaction problem can be viewed the problem of determining.
D2L(x; y) D. Â b a a c. Ã is not necessarily to be negative-definite for any a 2 R and b, c > 0. .... function P(x) = W(x) F(x) is the total action of the ..... Ys D fy 2 Rm :.
application of conventional duality theory can lead to distorted empirical results if
... Key words: duality theory, microeconomic theory applications, optimization.
Feb 7, 2007 - Convex Optimization. A convex optimization problem with variables x: minimize f0(x) subject to fi(x) ⤠0, i = 1, 2,...,m. aT i x = bi, i = 1, 2,...,p.
when F is a set-valued mapping), then / is said to be subdifferentiable at x0. It is obvious from the definitions of conjugate maps and subgradients that T ââ/(x) ...
Feb 7, 2007 - Thanks: Stephen Boyd (some materials and graphs from Boyd and. Vandenberghe) .... Lagrange dual function: g(λ, ν) = infx L(x, λ, ν) .... Strong duality: can price the violations so that there is no arbitrage advantages ...
Apr 25, 2015 - in operations research and mathematical finance. The second part ...... In Nonlinear operators and the calculus of variations (Sum- mer School ...
ًPق inf x∈X fًf1ًxق − f2ًxقق ًg1ًAxق − g2ًAxققg, where f1, f2, g1, and g2 are ...
Department of Mathematics, College of Sciences, King Saud University, P.O. Box
... §Department of Applied Mathematics, The Hong Kong Polytechnic University, ...
1.4.4 The Mehrotra predictor-corrector algorithm . ..... A fundamental difficulty in optimization is that it is not possible to solve all problems ef- ficiently. Indeed .... n decision variables under a set of linear (equality or inequality) constrai
a Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India ... Abstract The second-order duality results for the invex composite optimization problem are ... Ahmad [8] considered a pair of MondâWeir type second ord
May 7, 2010 - b â Rm being obtained, namely. (DL). Max. (λ,z,v)âBL. hL(λ,z,v),. 2 ... polyhedral set, via [9, Theorem 19.3] we get that L(A) is polyhedral, too.
May 7, 2005 - defined dual problems for differentiable multiobjective programming ... being suitable to define duals to nonconvex programming problems.
May 7, 2002 - W. Römisch: Humboldt University Berlin, Institute of Mathematics, D-10099 Berlin, Germany, e-mail: ...... Systems of the Deutsche Forschungsgemeinschaft. ... Oper. Res. 43, 477â490 (1995). 20. Rockafellar, R.T.: Duality and ...
May 1, 2010 - [4] M. Maddah-Ali, A. Motahari, and A. Khandani, âCommunication over ... [14] A. S. Motahari and A. K. Khandani, âCapacity bounds for the ...
Jan 29, 2003 - We shall show that they are subdifferentiable and we shall find a representation of some of their subgradients. The key element of the analysis ...
2-cell imbedded in a surface of demigenus d > 0 (the demigenus is equal to 2 minus .... in G, and Dâ is the edge set of a circle in Gâ, then the following are true.
Sep 15, 2008 - Programming, Strict Complementarity, Nice Cones, Devious Cones. ..... Moreover, similar to part 2, we can choose ¯s, ¯x appropriately, and ...
integration and optimization of local alternative renewable energy sources is an optional solution of the problem. in this paper we have studied the energetic ...
Dec 6, 2006 - duality theorems for differentiable fractional minimax programming. ... minimax programming problems in a Banach space; he established ...
which sufficient structure survives to explain the puzzles such as quark ..... condensation in RCD vacuum leads to the generalized Meissner effect which dictates ...
Dec 3, 2018 - k[y1,...,yd] is a strongly stable ideal with deg(m) ⤠n for all m â G(Iâ). An ...... nal of Pure and Applied Algebra 221 (2017), 1218â1241.
the mixed type duality results for nondifferentiable nonlinear programming prob ..... differentiable programs considered in section 3, and hence in view of various.
DUALITY AND ALTERNATIVE IN MULTIOBJECTTVE OPTIMIZATION ...
Denote by WP the set of all minimal elements u in Vp such that « = inf U for a certain U E Vp, U ¥= 0 and U totally ordered. Similarly, denote by WD the set of all ...
PROCEEDINGS Ol' THE AMERICAN MATHEMATICAL SOCIETY Volume 64, Number 2, lune 1977
DUALITY AND ALTERNATIVEIN MULTIOBJECTTVEOPTIMIZATION ELEMER E. ROSINGER Abstract. Within a general framework containing multiobjective optimization, an equivalence between duality properties and alternative conditions is established for pairs of constrained optimization problems. Sufficient conditions for a Pareto type duality and a multiobjective strong duality are
obtained.
1. Introduction. In a recent paper, McLinden [2] presented in the case of scalar optimization a general equivalence between duality and alternative, which underlies various known specific instances. The present paper extends McLinden's approach to the case of multiobjective optimization. Moreover, the multiobjective functions are replaced by a somewhat more general framework involving "level sets". Concerning the way one can associate to a given primal multiobjective optimization problem a convenient dual one, the "conjugate" construction in [4] and [1], extending Fenchel's approach, can be used. By this means, the main result in [4] (Theorem 2) can be seen to fall within the general framework presented in this paper.
2. Primal and dual constrained multiobjective optimization problems. Assume the partially ordered set (P, < o), contradicting the reflexivity of
