We consider computing the saddle points of a convex-concave function using subgradient methods. The existing literature on finding saddle points has mainly focused on establishing convergence properties of the generated iterates under some restrictive assumptions. In this paper, we propose a subgradient algorithm for generating approximate saddle points and provide per-iteration convergence rat...

For a multidimensional control problem (P)K involving controls u ∈ L∞, we construct a dual problem (D)K in which the variables ν to be paired with u are taken from the measure space rca (Ω, B) instead of (L∞)∗. For this purpose, we add to (P)K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

The aim of this study is to investigate the effects of corporate governance mechanisms in preventing the bankruptcy of companies listed in Tehran Stock Exchange. For this purpose, corporate governance mechanisms, including institutional ownership, non-executive members of the board, CEO dual responsibility and free float stock are determined as independent variables and Bankruptcy based on the ...

The classic paper of Shapley and Shubik (1971) characterized the core assignment game using ideas from matching theory LP-duality their highly non-trivial interplay. Whereas this is always non-empty, that general graph can be empty. This salvages situation by giving an imputation in 2/3-approximate for latter; moreover computed polynomial time. bound best possible, since it integrality gap natu...

This paper deals with approximate solutions of a nonsmooth semi-infinite programming multiple interval-valued objective functions. We first introduce four types quasi Pareto the considered problem by considering lower-upper interval order relation and then apply some advanced tools variational analysis generalized differentiation to establish necessary optimality conditions for these solutions....

the influence of social conditions on literature is an issue that many critics and scholars confirm and prove it; as duality is one of the manifestations of the influence of social conditions on the poet. it means that whenever the ambitions and beliefs of poet opposes the social facts, the duality will manifests in his poetry. the reality that the contemporary poets live in, imposes strong con...

• The dual problem is always convex no matter if the primal problem is convex, i.e., g is always concave. • The primal and dual optimal values, f∗ and g∗, always satisfy weak duality: f∗ ≥ g∗. • Slater’s condition: for convex primal, if there is an x such that h1(x) < 0, · · · , hm(x) < 0 and l1(x) = 0, · · · , lr(x) = 0 (12.5) then strong duality holds: f∗ = g∗. Note that the condition can be ...