In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...

Any real number x in the unit interval can be expressed as a continued fraction x = [n1, ..., nN , ...]. Subsets of zero measure are obtained by imposing simple conditions on the n N . By imposing n N ≤ m ∀ N ∈ IN , Jarnik defined the corresponding sets Em and gave a first estimate of dH(Em), dH the Hausdorff dimension. Subsequent authors improved these estimates. In this paper we deal with dH(...

A Multi-item inventory model with increasing holding cost, under available limited storage space and total investment cost is considered in this paper. The varying holding cost is considered to be a continuous function of production quantity. A demand dependent on unit cost has been considered and this unit cost is taken in fuzzy environment. The model is solved using Kuhn-Tucker conditions met...

The interval linear programming (IvLP) 1 is a method for decision making under uncertainty. A weak feasible solution to IvLP is called weakly optimal if it is optimal for some scenario of the IvLP. One of the basic and difficult tasks in IvLP is to check whether a given point is weak optimal. In this paper, we investigate linear programming problems with interval right-hand side. Some necessary...

We give a new, combinatorial proof for the necklace splitting problem for two thieves using only Tucker's lemma (a combinatorial version of the Borsuk-Ulam theorem). We show how this method can be applied to obtain a related recent result of Simonyi and even generalize it. 1 Necklace Splitting This paper was inspired by the combinatorial proof of Matou2ek [7] of the Lovász-Kneser theorem [6]. H...

Abstract. In this paper, we investigate the optimal control of the Burgers equation. For both optimal distributed and (Neumann) boundary control problems, the Dubovitskii and Milyutin functional analytical approach is adopted in investigation of the Pontryagin maximum principles of the systems. The necessary optimality conditions are, respectively, presented for two kinds of optimal control pro...

Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the normal cones, and thereby we provide some characterizations for convex generalized equations to have the metric subregularity. As applications, we establish formulas of the modulus ...

The paper presents necessary optimality conditions of Pontryagin’s type for infinite-horizon optimal control problems for age-structured systems with stateand control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a “complete” set of optimality conditions is missing in the existing literature, because it is problematic to ...

A global error bound is given on the distance between an arbitrary point in the n-dimensional real space R n and its projection on a nonempty convex set determined by m convex, possibly nondiierentiable, inequalities. The bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition constant that embodies a single strong Slater con...