Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martínez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CP...

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We also develop a s...

In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating MPEC through a KKT condition, this formulation has the advantage that it does not involve extra multipliers as new variables, and it usually requires weaker a...

We consider symmetrized KKT systems arising in the solution of convex quadratic programming problems in standard form by Interior Point methods. Their coefficient matrices usually have 3×3 block structure and, under suitable conditions on both the quadratic programming problem and the solution, they are nonsingular in the limit. We present new spectral estimates for these matrices: the new boun...

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner step...

In this paper, we present an adaptive relay assignment and power allocation algorithm in cognitive radio networks is proposed by using cooperative relay technologies which can improve the capacity of the cognitive system and extend coverage area. This algorithm converges faster than classic algorithms. The main target of the adaptive algorithm is to maximize each user’s capacity while guarantee...

A recently proposed trust-region approach for bound-constrained nonlinear equations is applied to the KKT systems arising from the discretization of a class of PDE-constrained optimization problems. Two different implementations are developed that take into account the large dimension and the special structure of the problems. The linear algebra phase is analyzed considering the possibility of ...

A Bayesian factor graph reduced to normal form (Forney, 2001) consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-divergence criterion using KKT conditions. The learning algorithms...

Nonconvex quadratic programming is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through...

1 Proofs Proof 1 (Proof of Proposition 1) The result for u∗ is straightforward (Allen et al., 2011). We consider the problem in v: maximize v u XRv−λ||v ||1 subject to v Rv ≤ 1 & vj ≥ 0 j = 1, . . . p. (1) As this problem is convex and Slater’s condition is satisfied, the KKT conditions are necessary and sufficient for optimality. These are given by the following: RX u−λ1(p) − 2γ∗ 1 Rv∗+~γ∗ 2 =...