In this paper we study necessary optimality conditions for the optimization problem infimumf0(x) subject to x ∈ S, where f0 : R → R is a polynomial function and S ⊂ R is a set defined by polynomial inequalities. Assume that the problem is bounded below and has the Mangasarian– Fromovitz property at infinity. We first show that if the problem does not have an optimal solution, then a version at ...

We derived the Kuhn-Tucker theorem by assuming regularity of the binding constraints. With the possibility of corner solutions, regularity is too stringent. The regularity condition will not necessarily apply throughout the constraint set. Verifying the regularity condition requires knowing the optimal solution, but the first-order conditions will not identify the optimal solution unless the re...

DC microgrids are growing in popularity due to their advantages terms of simplicity and energy efficiency while connecting dc sources loads. In traditional hierarchical schemes, optimization control implemented at different time scales. The loose integration lowers its makes it hard achieve real-time optimization. Even a slight disturbance can result deviations bus voltages output currents from...

To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483–500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush–Kuhn– Tucker (KKT)-type necessary conditions of multiobjective optimiz...

This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipsch...

Investigation of optimality conditions has been one the most interesting topics in theory multiobjective optimisation problems (MOP). To derive necessary MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) efficient and general assumption for scalar objective problems; however, GCQ does not ensure Karush-Kuhn Tucker (KKT)...

This paper studies first order conditions (Karush–Kuhn–Tucker conditions) for discretized optimal control problems with nonsmooth constraints. We present a simple condition which can be used to verify that a local optimal point satisfies the first order conditions and that a point satisfying the first order conditions is a global or local optimal solution of the optimal control problem.

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...

The generalized bilevel programming problem (GBLP) is a bilevel mathematical program where the lower level is a variational inequality. In this paper we prove that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decision variable, then using certain uniform parametric error bounds as penalty functions giv...

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...