This paper considers the minimization of a convex integral functional over the positive cone of an Lp space, subject to a finite number of linear equality constraints. Such problems arise in spectral estimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constra...

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic ...

In this paper a methodology for estimation in kernel-induced feature spaces is presented, making a link between the primal-dual formulation of Least Squares Support Vector Machines (LS-SVM) and classical statistical inference techniques in order to perform linear regression in primal space. This is done by computing a finite dimensional approximation of the kernel-induced feature space mapping ...

• 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 ...

In a recent work [3] the authors improved one of the most efficient interior-point approaches for some classes of block-angular problems. This was achieved by adding a quadratic regularization to the logarithmic barrier. This regularized barrier was shown to be self-concordant, thus fitting the general structural optimization interior-point framework. In practice, however, most codes implement ...

We observe a curious property of dual versus primal-dual path-following interior-point methods when applied to unbounded linear or conic programming problems in dual form. While primal-dual methods can be viewed as implicitly following a central path to detect primal infeasibility and dual unboundedness, dual methods can sometimes implicitly move away from the analytic center of the set of infe...

Dual-primal FETI methods for linear elasticity problems in three dimensions are considered. These are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations, whereas most of the constraints are enforced by Lagrange multipliers. An algorithmic framework for dualprimal FETI methods is describe...

A primal index of productivity change is introduced which decomposes exactly in three components: technical change, technical efficiency change and average scale economies (radial scale change). The proposed index is invariant to movement along indifference surfaces and it collapses to the Malmquist index if the technology is locally constant returns to scale. It is the best linear approximatio...