We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing suitable qualification, we formulate both necessary sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity assumptions, state strong, weak converse duality relations ...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that star(domA)∩ int domB 6= ∅, and A is of type (FPV). We sh...

We consider infinite-dimensional convex minimization problems with pointwise inequality constraints. We do not impose a constraint qualification condition, so that first-order necessary conditions are not available. To handle such problems we propose a method which combines advantages both from well-known penalty and barrier methods. For solving the resulting subproblems we develop a Newton-typ...

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...

This article revisits the maximum entropy algorithm in the context of recovering the probability distribution of an asset from the prices of finitely many associated European call options via partially finite convex programming. We are able to provide an effective characterization of the constraint qualification under which the problem reduces to optimizing an explicit function in finitely many...

We consider the problem of minimizing an extended-valued convex function on a locally convex space subject to a finite number of linear (in)equalities. When the standard constraint qualification fails a reduction technique is needed to derive necessary optimality conditions. Facial reduction is usually applied in the range of the constraints. In this paper it is applied in the domain space, thu...

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem uncertain data in the constraints. We first introduce SOCP dual polytopic sets. Then, obtain zero duality gap result between and its terms of new type characteristic cone constraint qualification. also construct norm-constrained sets corresponding them. Moreover, some numer...

Determination of a protein’s structure can facilitate an understanding of how the structure changes when that protein combines with other proteins or smaller molecules. In this paper we study a semidefinite programming (SDP) relaxation of the (NP-hard) side chain positioning problem (SCP) presented in Chazelle et al. [4]. We show that the Slater constraint qualification (SCQ) fails for the SDP ...

The purpose of this paper is to consider the Mond-Weir type dual model for a class of non-smooth multiobjective semi-infinite programming problem. In this work, we use generalization of convexity namely ( , ) G F θ − convexity and Kuhn-Tucker constraint qualification, to prove new duality results for such semi-infinite programming problem. Weak, strong and converse duality theorems are derived....

We present a strong duality theory for optimization problems over symmetric cones without assuming any constraint qualification. We show important complexity implications of the result to semidefinite and second order conic optimization. The result is an application of Borwein and Wolkowicz’s facial reduction procedure to express the minimal cone. We use Pataki’s simplified analysis and provide...