In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...

We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular-value decomposition, we derive a modified primal-dual optimality system whose solution is locally unique, n...

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. much harder version under recent consideration to enforce bounds constraints on the polynomial. In this paper, we consider of constructioning such approximations using polynomials Bernstein basis. We a family inequality-constrained quadratic programs. univariate case, cone cons...

In a 1918 paper [Sch18], Schur proved a remarkable inequality that related group representations, Hermitian forms and determinants. He also gave concise necessary and sufficient conditions for equality. In [Mar64], Marcus gave a beautiful short proof of Schur’s inequality by applying the Cauchy-Schwarz inequality to symmetric tensors, but he did not discuss the case of equality. In [Wil69], Wil...

in this paper we consider contact cr-warped product submanifolds of the type $m = n_ttimes_f n_perp$, of a nearly kenmotsu generalized sasakian space form $bar m(f_1‎, ‎f_2‎, ‎f_3)$ and by use of hopf's lemma we show that $m$ is simply contact cr-product under certain condition‎. ‎finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case i...

Lagrangian methods are popular in solving continuous constrained optimization problems. In this paper, we address three important issues in applying Lagrangian methods to solve optimization problems with inequality constraints. First, we study methods to transform inequality constraints into equality constraints. An existing method, called the slack-variable method, adds a slack variable to eac...

Abstract: This study proposes a novel chaotic quantum-behaved particle swarm optimization (CQPSO) algorithm for solving shortterm hydrothermal scheduling problem with a set of equality and inequality constraints. In the proposed method, chaotic local search technique is employed to enhance the local search capability and convergence rate of the algorithm. In addition, a novel constraint handlin...

‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...