Bilevel programs are optimization problems which have a subset of their variables constrained to be an optimal solution of another problem parameterized by the remaining variables. They have been applied to decentralized planning problems involving a decision process with a hierarchical structure. This paper considers the linear fractional/quadratic bilevel programming (LFQBP) problem, in which...

Abstract. A multi-objective inventory model with demand dependent unit cost and leading time has been formulated with storage space, number of orders and production cost as constraints. In most of the real world situations the cost parameters the objective function and constraints of the decision makers are imprecise in nature. A demand dependent unit cost is assumed and solved using Karush Kuh...

This paper presents a model predictive approach for collision avoidance of car-like robots. An optimal problem is formulated in terms of cost minimization under constraints. Information on each robot can be incorporated online in the nonlinear model predictive framework and kinematic constraints are treated by Karush-Kuhn-Tucker(KKT) condition. For distributed collision avoidance of multiple ro...

We describe a primal-dual interior point algorithm for a class of convex separable programming problems subject to linear constraints. Each iteration updates a penalty parameter and finds a Newton step associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem for that parameter. It is shown that the duality gap is reduc...

For an implicit multifunction (p) defined by the generally nonsmooth equation F(x, p) = 0, contingent derivative formulas are derived, being similar to the formula ′ = −Fx−1Fp in the standard implicit function theorem for smooth F and . This will be applied to the projection X(p) = {x | ∃y: (x, y) ∈ (p)} of the solution set (p) of the system F(x, y, p) = 0 onto the x-space. In particular settin...

Considering the minmax programming problem, lower and upper subdifferential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely different from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained are closed to...

This paper introduces a software tool SYM-LS-SVM-SOLVER written in Maple to derive the dual system and the dual model representation of LS-SVM based models, symbolically. SYM-LS-SVM-SOLVER constructs the Lagrangian from the given objective function and list of constraints. Afterwards it obtains the KKT (Karush-Kuhn-Tucker) optimality conditions and finally formulates a linear system in terms of...

‎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...

We consider a discrete bridge from (0, 0) to (2N, 0) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order N with α > 0. We provide a classification of the static and dynamic behaviour of this model according to the value of the parameter α. Our main results concern the hydrodynamic limit and the fluctuations of the bridge. For α < 1,...

We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.