We consider the analysis operator and synthesis dictionary learning problems based on the the `1 regularized sparse representation model. We reveal the internal relations between the `1-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is t...

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We express the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimizatio...

In this paper, we propose a generic branch-and-cut algorithm for a special class of bi-level combinatorial optimization problems. Namely, we study such problems that can be reformulated as bilinear min-max combinatorial optimization problems. We show that the reformulation can be efficiently solved by a branch-and-cut algorithm whose cuts represent the inner maximization feasibility set. The al...

We consider the analysis operator and synthesis dictionary learning problems based on the the `1 regularized sparse representation model. We reveal the internal relations between the `1-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is t...

This paper presents a methodology to develop an optimal coordinated bidding strategy of a supplier considering hourly price-volume bid in Day-Ahead Energy Market (DAEM) and Balancing Energy market (BEM). In this work, a bi-level optimization problem has been proposed considering rivals’ bidding behavior, inter temporal constraints, and multi period auction. Lower level problem represents the ma...

This paper proposes a novel approach to generate a uniform distribution of the optimal solutions along the Pareto frontier. We make use of a standard mathematical technique for optimization namely line search and adapt it so that it will be able to generate a set of solutions uniform distributed along the Pareto front. To validate the method, numerical bi-criteria examples are considered. The m...

Crack identification is a very important issue in mechanical systems, because it is a damage that if develops may cause catastrophic failure. In the first part of this research, modal analysis of a multi-cracked variable cross-section beam is done using finite element method. Then, the obtained results are validated usingthe results of experimental modal analysis tests. In the next part, a nove...

the decomposition $gamma=bh$ of a group $gamma$ into a subset $b$ and a subgroup $h$ of $gamma$ induces, under general conditions, a group-like structure for $b$, known as a gyrogroup. the famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary operation given by t...

The difficulty to solve multiple objective combinatorial optimization problems with traditional techniques has urged researchers to look for alternative, better performing approaches for them. Recently, several algorithms have been proposed which are based on the Ant Colony Optimization metaheuristic. In this contribution, the existing algorithms of this kind are reviewed and experimentally tes...

In this paper, the bi-directional evolutionary structural optimization (BESO) method is used to find optimal layouts of 3D prestressed concrete beams. Considering the element sensitivity number as the design variable, the mathematical formulation of topology optimization is developed based on the ABAQUS finite element software package. The surface-to-surface contact with a small sliding between...