We consider the problem of packing squares with profits into a bounded square region so as to maximize their total profit. More specifically, given a set L of n squares with positive profits, it is required to pack a subset of them into a unit size square region [0;1℄ [0;1℄ so that the total profit of the squares packed is maximized. For any given positive accuracy ε > 0, we present an algorith...

BACKGROUND Left ventricular (LV) function is dependent on load, intrinsic contractility and relaxation with a variable impact on specific mechanics. Strain (ε) imaging allows the assessment of cardiac function; however, the direct relationship between volume and strain is currently unknown. The aim of this study was to establish the impact of preload reduction through head-up tilt (HUT) testing...

In this paper, we present a solution to the constrained l1-norm minimization problem for sparse SAR imaging. The techniques rely on the recent advances in the solution of optimization problems, based on the Augmented Lagrangian Methods (ALMs), namely the Alternating Direction Method of Multipliers. Here, we present an application of CSALSA (an ALM for constrained optimization problems) to SAR i...

We define a primal-dual algorithm model (SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exact augmented Lagrangian function and the use ...

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global ...

In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the MangasarianFromovitz and the basic constraint qualifi...

Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. A new condition of this type is introduced in the present paper. It will be proved that ...

Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of constraints that make problems hard for evolutionary algorithm. In our study, we examine how various sets of constraints can influence the behaviour of ε-Constra...

In this section, we derive in detail the closed form solution of problem (12) for binary pairwise factors (Sect. 4.1). Recall that the marginal polytope M(G a) is given by:

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictorcorrector continuation are described. In the first phase of this method...