Duality theorems for perturbed convex optimization

-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

WEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

weak and strong duality theorems for fuzzy conic optimization problems

the objective of this paper is to deal with the fuzzy conic program- ming problems. the aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. toward this end, the convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. un- der this setting, duality t...

Convex Optimization and Lagrangian Duality

Finally the Lagranage dual function is given by g(~λ, ~ν) = inf~x L(~x,~λ, ~ν) We now make a couple of simple observations. Observation. When L(·, ~λ, ~ν) is unbounded from below then the dual takes the value −∞. Observation. g(~λ, ~ν) is concave1 as it is the infimum of a set of affine2 functions. If x is feasible solution of program (10.2)(10.4), then we have the following L(x,~λ, ~ν) = f0(x)...

COM524500 Optimization for Communications Summary: Convex Optimization and Duality 1 Convex Optimization

fi(x) < 0, i = 1, . . . ,m, hi(x) = 0, i = 1, . . . , p i.e., all inequality constraints are inactive. • A problem is feasible if there exists x ∈ C; infeasible if C = ∅; and strictly feasible if there is a strictly feasible point. • A problem is unconstrained if C = R. • The quantity p = inf{f0(x) | x ∈ C} is called the optimal value (of the associated problem). We use p = +∞ to represent the ...