In this paper we consider the strategy of stochastic bundling, which we define as a selling strategy in which firms guarantee a consumer will receive a good, but do not guarantee which one it will be. First we derive a new condition that ensures the optimality of stochastic bundling when there is no secondary market. Then we graphically consider the conditions under which stochastic bundling ma...

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every M...

In this paper we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints (MPECs). We first show that MPEC-LICQ is not a constraint qualification for the strong (S-) stationary condition when the objective function is nonsmooth. Enhanced Fritz John conditions provide stronger necessary optimality conditions under weaker constraint qualifications. In...

The quest for optimal/stable paths in graphs has gained attention in a few practical or theoretical areas. To take part in this quest this chapter adopts an equilibrium-oriented approach that is abstract and general: it works with (quasi-arbitrary) arc-labelled digraphs, and it assumes very little about the structure of the sought paths and the definition of equilibrium, i.e. optimality/stabili...

The goal of self-optimising control is to select a set of controlled variables, which when kept at constant setpoints, indirectly lead to suboptimal operation. Based on the necessary condition of unconstrained optimisation, Cao (2004) has identified that the steady-state optimizing control for unconstrained degrees of freedom is to keep a dimension-reduced gradient at zero. Alternatively, two s...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

The objective of this work is to try to define and calculate the optimal growth path, in the presence of exogenous technical change, without resorting to the discounted-sum criterion. The solution suggested is to consider an optimality criterion expressing an Allais-anonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decom...

The well-known and established global optimality conditions based on the Lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero. We develop a set of global optimality conditions which are structurally similar but which are consistent for any size of the duality gap. This system characterizes a primal–dual optimal solution by means of primal and d...

An experimental design is said to be Schur optimal, if it is optimal with respect to the class of all Schur isotonic criteria, which includesKiefer’s criteria of p-optimality, distance optimality criteria andmany others. In the paper we formulate an easily verifiable necessary and sufficient condition for Schur optimality in the set of all approximate designs of a linear regression experiment w...