Sharp interface limit of a multi-phase transitions model under nonisothermal conditions

A vectorial Modica–Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain $$\Omega $$ Ω . The mass constrained minimization problem and the case of Dirichlet boundary conditions are also treated. The proofs rely on the precise understanding of minimizing geodesics for the degenerate metric induced by the potential.

A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting

In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

This work presents an approach to spacecraft attitude motion planning which guarantees rest-to-rest maneuvers while satisfying pointing constraints. Attitude is represented on the group of three dimensional rotations. The angular velocity is expressed as weighted sum of some basis functions, and the weights are obtained by solving a constrained minimization problem in which the objective is the maneuvering time. However, the analytic expressions of objective and constraints of this minimization problem are not available. To solve the problem despite this obstacle, we propose to use a derivative-free approach based on sequential penalty. Moreover, to avoid local minima traps during the search, we propose to alternate phases in which two different objective functions are pursued. The control torque derived from the spacecraft inverse dynamics is continuously differentiable and vanishes at its endpoints. Results on practical cases taken from the literature demonstrate advantages over existing approaches.

Multicomponent multiphase reactive fluid flow in viscoelastoplastic porous media: localization patterns of fluid flow and strain

<p>This work is devoted to developing the self-consistent thermo-hydro-chemo-mechanical reactive transport model to predict and describe natural and industrial petroleum processes at different scales.</p><p>We develop a version of the front tracking approach for multicomponent multiphase flow in order to treat spontaneous splitting of discontinuities. We revisit the solution for the Riemann problem and systematically classify all possible configurations as functions of initial concentrations on both sides of the discontinuity. We validate the algorithm against finite volume high-resolution technics and high-order spectral finite elements.</p><p>To calculate the parameters of phase equilibria, we utilize an approach based on the direct minimization of the Gibbs energy of a multicomponent mixture. This method ensures the consistency of the thermodynamic lookup tables. The core of the algorithm is the non-linear free-energy constrained minimization problem, formulated in the form of a linear programming problem by discretization in compositional space.</p><p>The impact of the complex rheological response of porous matrix on the morphology of fluid flow and shear deformation localization is considered. Channeling of porosity waves and shear bands morphology and their orientation is investigated for viscoelastoplastic both shear and bulk rheologies.</p>

On the minimum-norm solution of convex quadratic programming

We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton's method to solve this problem. Numerical results show that the proposed method is efficient.

Negentropy-Based Sparsity-Promoting Reconstruction with Fast Iterative Solution from Noisy Measurements

Compressed sensing provides an elegant framework for recovering sparse signals from compressed measurements. This paper addresses the problem of sparse signal reconstruction from compressed measurements that is more robust to complex, especially non-Gaussian noise, which arises in many applications. For this purpose, we present a method that exploits the maximum negentropy theory to promote the adaptability to noise. This problem is formalized as a constrained minimization problem, where the objective function is the negentropy of measurement error with sparse constraint ℓp(0<p<1)-norm. On the minimization issue of the problem, although several promising algorithms have been proposed in the literature, they are very computationally demanding and thus cannot be used in many practical situations. To improve on this, we propose an efficient algorithm based on a fast iterative shrinkage-thresholding algorithm that can converge fast. Both the theoretical analysis and numerical experiments show the better accuracy and convergent rate of the proposed method.

The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem

This work analyzes the alternating minimization (AM) method for solving double sparsity constrained minimization problem, where the decision variable vector is split into two blocks. The objective function is a separable smooth function in terms of the two blocks. We analyze the convergence of the method for the non-convex objective function and prove a rate of convergence of the norms of the partial gradient mappings. Then, we establish a non-asymptotic sub-linear rate of convergence under the assumption of convexity and the Lipschitz continuity of the gradient of the objective function. To solve the sub-problems of the AM method, we adopt the so-called iterative thresholding method and study their analytical properties. Finally, some future works are discussed.