The T ∗ ε integral was calculated numerically along an extending, tunneling crack front in an 8 mm thick, aluminum three-point bend (3PB) specimen, using a numerical model driven by experimentally obtained surface displacements. The model provided input to a contour integration for the T ∗ ε integral, via the Equivalent Domain Integral (EDI) method with incremental plasticity. Validity of the a...

Abstract. We propose a smoothing quadratic regularization (SQR) method for solving box constrained optimization problems with a non-Lipschitz regularization term that includes the lp norm (0 < p < 1) of the gradient of the underlying image in the l2-lp problem as a special case. At each iteration of the SQR algorithm, a new iterate is generated by solving a strongly convex quadratic problem wit...

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate...

A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. We discuss in this paper augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discu...

The thermo-hydraulic behavior of the air flow over a two dimensional ribbed channel wasnumerically investigated in various rib-width ratio configurations (B/H=0.5-1.75) atdifferent Reynolds numbers, ranging from 6000 to 18000. The capability of differentturbulence models, including standard k-ε, RNG k-ε, standard k-ω, and SST k-ω, inpredicting the heat transfer rate was compared with the experi...

A constrained optimization method, called the Lagrange-Hoppeld (LH) method, is presented for solving Markov random eld (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian mul-tiplier technique with the Hoppeld network to solve a constrained optimization problem into which the original Bayesian estimation problem is reform...

The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic development of constrained optimization. In this paper, we mainly show that Nesterov’s influential acceleration techniques can be applied to accelerate ALM, thus yielding an accelerated ALM whose iteration-complexity is O(1/k) for linearly constrained convex programming. As a by-product, we also show easily ...

The alternating direction method of multipliers (ADMM) is a common optimization tool for solving constrained and non-differentiable problems. We provide an empirical study of the practical performance of ADMM on several nonconvex applications, including `0 regularized linear regression, `0 regularized image denoising, phase retrieval, and eigenvector computation. Our experiments suggest that AD...

Algencan is a freely available piece of software that aims to solve smooth large-scale constrained optimization problems. When applied to specific problems, obtaining a good performance in terms of efficacy and efficiency may depend on careful choices of options and parameters. In the present paper the application of Algencan to four portfolio optimization problems is discussed and numerical re...

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an Outer Trust-Region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones and ...