Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type … Read more
An extension of a proximal point algorithm for difference of two convex functions is presented in the context of Riemannian manifolds of nonposite sectional curvature. If the sequence generated by our algorithm is bounded it is proved that every cluster point is a critical point of the function (not necessarily convex) under consideration, even if … Read more
In this article, a hybrid Lagrangean metaheuristic is proposed for single machine scheduling problems with sequence-dependent setup times and due dates. The objective function considered throughout this work, is to minimize the total tardiness. Related works and taxonomies for hybrid metaheuristics are analyzed, through a thorough historical overview. The proposed hybrid Lagrangean metaheuristic is a … Read more
Risk adjustment is used to calibrate payments to health plans based on the relative health status of insured populations and helps keep the health insurance market competitive. Current risk adjustment models use parameter estimates obtained via regression and are thus subject to estimation error. This paper discusses the impact of parameter uncertainty on risk scoring, … Read more
We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset allocations are not precisely known to the investment manager. In this paper, we propose a robust framework that takes into account the uncertainty stemming from the fund managers’ allocation, as well as the more … Read more
In this paper we present a mathematical programming approach to tighten a Big-$M$ formulation ($P_M$) of a Mixed Integer Problem with Logical Implications ($P$). If $M_0$ is a valid vector (the optimal solutions of $P$ belong to the feasible solutions set of $P_{M_0}$) our procedures find a valid vector $M$ such that $M \leq M_0$. … Read more
In this paper, two homotopy methods, which combine the advantage of the homotopy technique with the effectiveness of the iterative hard thresholding method, are presented for solving the compressed sensing problem. Under some mild assumptions, we prove that the limits of the sequences generated by the proposed homotopy methods are feasible solutions of the problem, … Read more
In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the L2−Lp minimization problem. We propose an iterative algorithm that decides the next iteration based on the local convexity/concavity/sparsity of its current position. We show that our algorithm finds an epsilon-KKT point within O(log(1/epsilon)) iterations. The same result is also … Read more
We propose a stochastic optimization model for the Multiperiod Multiproduct Advertising Budgeting problem, so that the expected profit of the advertising investment is maximized. The model is a convex optimization problem that can readily be solved by plain use of standard optimization software. It has been tested for planning a realistic advertising campaign. In our … Read more
The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since L-BFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a … Read more