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The aim of this study is to develop a hybrid genetic algorithm (H-GA) that combines a genetic algorithm (GA) and a descent local search technique to pursue the optimization of a sandwich composite inter-stage skirt located in the upper bound of the launcher. Total number of plies forming the sandwich composite skin and fiber orientations (predefined ply angles) are considered as design variables. The H-GA is chosen as an optimization tool thanks to its ability to deal with discrete optimization problems, of which the design of composites stacking is an example. First, the proposed approach is presented and explained. Then, its performances are compared and discussed against those offered by the classical GA.The aim of this study is to develop a hybrid genetic algorithm (H-GA) that combines a genetic algorithm (GA) and a descent local search technique to pursue the optimization of a sandwich composite inter-stage skirt located in the upper bound of the launcher. Total number of plies forming the sandwich composite skin and fiber orientations (predefined ply angles) are considered as design variables. The H-GA is chosen as an optimization tool thanks to its ability to deal with discrete optimization problems, of which the design of composites stacking is an example. First, the proposed approach is presented and explained. Then, its performances are compared and discussed against those offered by the classical GA.

Objective The presence of testicular appendices was prospectively evaluated in 89 boys with 96 undescended testes who underwent orchidopexy over the period of 4 years. Results The patients were divided into two groups. Group A included 42 boys with 49 undescended testes positioned close to the internal inguinal ring, and Group B included 47 boys with 47 undescended testes close to the external inguinal ring. The incidence of appendix testis (AT) in Group A was 57.1% (28 in 49) and 78.7% (37 in 47) in Group B. The results of our study showed significantly decreased incidence of testicular appendices in undescended testes positioned close to the internal inguinal ring compared with undescended testes positioned close to the external inguinal ring (p < 0.05). Conclusion AT may play a role in normal testicular descent and the undescended testis positioned close to the external inguinal ring can be considered as a separate entity of the true congenital undescended testis.

In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a player's strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms., Comment: IJCAI 2019, 11 pages, 1 figure

Recent research in machine learning pointed to the core problem of state-of-the-art models which impedes their widespread adoption in different domains. The models' inability to differentiate between noise and subtle, yet significant variation in data leads to their vulnerability to adversarial perturbations that cause wrong predictions with high confidence. The study is aimed at identifying whether the algorithms inspired by biological evolution may achieve better results in cases where brittle robustness properties are highly sensitive to the slight noise. To answer this question, we introduce the new robust gradient descent inspired by the stability and adaptability of biological systems to unknown and changing environments. The proposed optimization technique involves an open-ended adaptation process with regard to two hyperparameters inherited from the generalized Verhulst population growth equation. The hyperparameters increase robustness to adversarial noise by penalizing the degree to which hardly visible changes in gradients impact prediction. The empirical evidence on synthetic and experimental datasets confirmed the viability of the bio-inspired gradient descent and suggested promising directions for future research. The code used for computational experiments is provided in a repository at https://github.com/yukinoi/bio_gradient_descent.

This paper presents a numerical algorithm for computing 6-degree-of-freedom free-final-time powered descent guidance trajectories. The trajectory generation problem is formulated using a unit dual quaternion representation of the rigid body dynamics, and several standard path constraints. Our formulation also includes a special line of sight constraints that is enforced only within a specified band of slant ranges relative to the landing site, a novel feature that is especially relevant to Terrain and Hazard Relative Navigation. We use the newly introduced state-triggered constraints to formulate these range constraints in a manner that is amenable to real-time implementations. The resulting non-convex optimal control problem is solved iteratively as a sequence of convex second-order cone programs that locally approximate the non-convex problem. Each second-order cone program is solved using a customizable interior point method solver. Also introduced are a scaling method and a new heuristic technique that guide the convergence process towards dynamic feasibility. To demonstrate the capabilities of our algorithm, two numerical case studies are presented. The first studies the effect of including a slant-range-triggered line of sight constraint on the resulting trajectories. The second study performs a Monte Carlo analysis to assess the algorithm's robustness to initial conditions and real-time performance., Comment: Submitted to the AIAA Journal of Guidance, Control, and Dynamics

This chapter focuses on switching regression for the identification of arbitrarily switched linear systems. It describes practical methods first dedicated to the minimization of the error for a fixed number of modes: the seminal algebraic approach, the continuous optimization approach, and a block-coordinate descent approach in the form of the simple but efficient k-LinReg algorithm. Then, the methods that aim at estimating the smallest number modes required to satisfy a given bound on the error are presented: the so-called bounded-error method at the origin of this viewpoint, another block-coordinate descent approach dedicated to this case, and several approaches based on sparsity arguments.

This paper addresses a new Mixed-model Assembly Line Sequencing Problem in the Footwear industry. This problem emerges in a large company, which benefits from advanced automated stitching systems. However, these systems need to be managed and optimised. Operators with varied abilities operate machines of various types, placed throughout the stitching lines. In different quantities, the components of the various shoe models, placed in boxes, move along the lines in either direction. The work assumes that the associated balancing problems have already been solved, thus solely concentrating on the sequencing procedures to minimise the makespan. An optimisation model is presented, but it has just been useful to structure the problems and test small instances due to the practical problems’ complexity and dimension. Consequently, two methods were developed, one based on Variable Neighbourhood Descent, named VND-MSeq, and the other based on Genetic Algorithms, referred to as GA-MSeq. Computational results are included, referring to diverse instances and real large-size problems. These results allow for a comparison of the novel methods and to ascertain their effectiveness. We obtained better solutions than those available in the company.

This paper presents a Parallel Block-Coordinate Descent (PBCD) algorithm for solving the user equilibrium traffic assignment problem. Most of the existing algorithms for the user equilibrium-based traffic assignment problem are developed and implemented sequentially. This paper aims to study and investigate the parallel computing approach to utilize the widely available parallel computing resources. The PBCD algorithm is developed based on the state-of-the-art path-based algorithm, i.e., the improved path-based gradient projection algorithm (iGP). The computationally expensive components in the iGP are identified and parallelized. A parallel block-coordinate method is proposed to replace the widely used Gauss-Seidel method for the procedure of path flow adjustment. A new rule is proposed to group OD pairs into different blocks. The numerical examples show that the implemented PBCD algorithm can significantly reduce the computing time.

The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied in this paper utilize dictionaries instead of a canonical basis used in the coordinate descent algorithms. We show how this approach allows us to reduce dimensionality of the problem. Also, we investigate which properties of a dictionary are beneficial for the convergence rate of typical greedy-type algorithms.

In this paper we study a hub location problem in which the hubs to be located must form a set of interconnecting lines. The objective is to minimize the total weighted travel time between all pairs of nodes while taking into account a budget constraint on the total set-up cost of the hub network. A mathematical programming formulation, a Benders-branch-and-cut algorithm and several heuristic algorithms, based on variable neighborhood descent, greedy randomized adaptive search, and adaptive large neighborhood search, are presented and compared to solve the problem. Numerical results on two sets of benchmark instances with up to 70 nodes and three lines confirm the efficiency of the proposed solution algorithms.

In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography.The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions.Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN.The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

In this paper, by incorporating a multi-step scheme into the doubly stabilized bundle method (DSBM) recently developed by Oliveira and Solodov (2016), we propose a multi-step doubly stabilized bundle method (MDSBM) for solving nonsmooth convex optimization problems. In contrast to a single sequence generated by DSBM, the MDSBM generates three related iteration sequences. One is used to build the cutting-planes model of the objective function, another is served as the stability centers, and the third is the sequence of solutions to our new doubly stabilized subproblems. In addition, we present a new descent test criterion, aiming to take advantage of the multi-step scheme. We establish global convergence of the proposed method, and finally present some promising numerical results.

The projection technique is a very important method and efficient for solving unconstraint optimization and nonlinear equations. In this study, we developed a Liu-Story (LS) algorithm for solving monotone equations of nonlinear systems. The new algorithm satisfies the sufficient descent condition and it’s a suitable method of large scale equations for its limited memory. We established a global convergence of suggest method under the mild conditions. Numerical results proved that the new algorithm works well and promising.

Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising.

Blind signal separation (BSS) has received much research attention due to its potential applicability in recent decades. A great deal of measurements acquired from practical application show some degree of periodicity. Information theoretic criterion is exploited to deduce an objective function for the separation of periodic signals. Minimizing the objective function with natural gradient descent rule, a novel learning algorithm is proposed correspondingly. Computer simulations on signals with temporal structure illustrate the efficiency of the proposed techniques.

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.

A novel method for automatic facial landmark localization is presented. The method builds on the supervised descent framework, which was shown to successfully localize landmarks in the presence of large expression variations and mild occlusions, but struggles when localizing landmarks on faces with large pose variations. We propose an extension of the supervised descent framework that trains multiple descent maps and results in increased robustness to pose variations. The performance of the proposed method is demonstrated on the Bosphorus, the FRGC and the UND data sets for the problem of facial landmark localization from 3D data. Our experimental results show that the proposed method exhibits increased robustness to pose variations, while retaining high performance in the case of expression and occlusion variations.

K-nearest neighbor graphs (K-NNGs) are used in many data-mining and machine-learning algorithms. Naive construction of K-NNGs has a complexity of O(n2), which could be a problem for large-scale data sets. In order to achieve higher efficiency, many exact and approximate algorithms have been developed, including the NN-Descent algorithm of Dong, Charikar and Li. Empirical evidence suggests that the practical complexity of this algorithm is in O(n1.14), which is a significant improvement over brute force construction. However, NN-Descent has a major drawback --- it produces good results only on data of low intrinsic dimensionality. This paper presents an experimental analysis of this behavior, and investigates possible solutions. We link the quality of performance of NN-Descent with the phenomenon of hubness, defined as the tendency of intrinsically high-dimensional data to contain hubs --- points with high in-degrees in the K-NNG. We propose two approaches to alleviate the observed negative influence of hubs on NN-Descent performance.

This paper introduces descent moment distributions for analysis of single and multi permutation codes defined via Levenshtein (VT) codes. Originally this work is motivated by computer experiments of deletion spheres for contant weight codes and the authors proved properties in a theoretical manner.

We use a numerical method to compute a database of three-point branched covers of the complex projective line of small degree. We report on some interesting features of this data set, including issues of descent., ANTS final revision

A new hybrid of the conjugate gradient (CG) method that combines the features of five different CG methods is proposed. The corresponding CG algorithm generated descent directions independent of line search procedures. With the standard Wolfe line search conditions, the algorithm was shown to be globally convergent. Based on numerical experiments with selected large-scale benchmark test functions and comparison with classical methods, the method is very promising and competitive.

Reconstruction of objects behind walls is a common problem in microwave imaging. So far, several algorithms such as time reversal MUSIC (TR-MUSIC) and linear sampling method (LSM) have been proposed. Such algorithms require Green's function of the background medium. In some applications, walls have surface roughness. This roughness should be accounted for in the Green's function computation. The Green's function of a wall with corrugated interfaces was derived and its effects on LSM was explored, previously. Here, it is used to implement TR-MUSIC algorithm. As shown in here, it is necessary to account for the wall corrugations in Green's function estimation in order to have descent TR images. To gain an insight into the problem, TR-MUSIC images are compared with those of LSM, using multistatic data matrices.

We want to solve fuzzy linear programming problems with fuzzy coefficients in the objective function using a new variable neighborhood search algorithm. In our proposed algorithm, the local search is defined based on descent directions. We make use of our recently proposed modified Kerre's method for finding descent directions. The fuzzy optimization problem is solved directly, without changing it to a crisp program. We show the effectiveness of our proposed method in comparison with some available methods by using a non-parametric statistical sign test. The objective function values obtained by our proposed method turn to be more accurate the ones obtained by other methods.

This paper presents a modified Wei-Yao-Liu conjugate gradient method, which automatically not only has sufficient descent property but also owns trust region property without carrying out any line search technique. The global convergence property for unconstrained optimization problems is satisfied with weak Wolfe-Powell (WWP) line search. Meanwhile, the present method can be extended to solve nonlinear equations problems. Under some mild condition, line search method and project technique, the global convergence is established. Some preliminary numerical tests are presented. The numerical results show its effectiveness.

This paper deals with the problem of generating optimal 2D flight paths compliant with mission constraints resulting from no-fly zones and/or obstacles, and from flight mechanics limitations as minimum coordinate turn radius and maximum climb and descent angles. The optimization problem is converted into a minimum cost path search within a so called Essential Visibility Graph whose arcs and corresponding weights are obtained via an efficient branching algorithm in view of possible real-time implementations. A possible extension to 3D paths is also presented. Finally, numerical examples are reported with a discussion on the computational aspects.

The most well-known technique or method in unconstrained optimization is the conjugate gradient method. It is used to get the greatest solution for the unconstrained optimization problems. This method is used in many fields especially, computer science, and engineering due to its convergence speed, simplicity, and the low memory requirements. A new modified conjugate gradient method is presented in this paper. This method is proved with the strong Wolfe-Powell (SWP) line search that it possesses sufficient descent property, and is globally convergent. Numerical results for a set of 141 test problems show the outperformance of the new proposed formula comparing with other methods using the same line search. The performance of this method is more efficient and better than the others.

In the present paper, we propose a modification of the method of bi-coordinate variations for network equilibrium problems with mixed demand. This method is based on the equilibrium conditions of the problem under consideration. It uses a special tolerance control and thresholds for constructing descent directions and a variant of the Armijo-type line-search procedure as a rule of step choice. Some results of preliminary numerical calculations which confirm efficiency of the method are also presented.

The conjugate gradient (CG) and Davidon, Fletcher and Powell (DFP) method are both well known solvers for solving unconstrained optimization problems. In this paper, we proposed a new hybrid DFP-CG method and compared with the ordinary DFP method in terms of number of iteration and CPU times. Numerical results show that the new algorithm is more efficient compared to the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Stochastic neural networks serve as general models useful for machine learning problems. Several models on discrete state spaces have been studied, and their proposed gradient estimation procedures are based on having closed form solutions for the resulting probability distributions. The methods exploit constraints on network connectivity, such as symmetry, or the absence of cycles. Our interest is in the general case of long-term average cost in networks with arbitrary connectivity, where only knowledge of the transition probabilities is available. We propose an algorithm that computes descent directions based on simultaneous perturbation analysis and measure valued differentiation.

A theory of cultural structures predicts the objects observed by anthropologists. We here define those which use kinship relationships to define systems. A finite structure we call a partially defined quasigroup (or pdq, as stated by Definition 1 below) on a dictionary (called a natural language) allows prediction of certain anthropological descriptions, using homomorphisms of pdqs onto finite groups. A viable history (defined using pdqs) states how an individual in a population following such history may perform culturally allowed associations, which allows a viable history to continue to survive. The vector states on sets of viable histories identify demographic observables on descent sequences. Paths of vector states on sets of viable histories may determine which histories can exist empirically.

A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based In-tree structure proves able to reveal the clustering structure underlying the dataset, except one imperfect place, that is, there are some undesired edges in this In-tree which require to be removed. Here, we propose an effective way to automatically remove the undesired edges in In-tree via an effective combination of the In-tree structure with affinity propagation (AP). The key for the combination is to add edges between the reachable nodes in In-tree before using AP to remove the undesired edges. The experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed method.

We address a home care service problem, and propose a three-phase metaheuristic based on Variable Neighborhood Decent algorithm and Longest Processing Time algorithm. In the first phase, we resolve the assignment problem using a scheduling algorithm which is the Longest Processing Time algorithm. In the second one, for each nurse, we resolve the routing problem in order to improve the travelled distances using the Variable Neighborhood Decent algorithm. The third phase, is devoted to refine the second phase in terms of maximizing patient's satisfaction regarding services rendered using an efficient heuristic that performs replacements of patients not satisfied between nurses if possible while taking into consideration the distances found in the second phase. The numerical results show the efficiency of the proposed three-phase approach.

The stochastic gradual descent method (SGD) is a popular optimization technique based on updating each θk parameter in the ∂J(θ)/∂θk direction to minimize / maximize the J(θ) cost function. This technique is frequently used in current artificial learning methods such as convolutional learning and automatic encoders. In this study, five different approaches (Momentum, Adagrad, Adadelta, Rmsprop ve Adam) based on SDA used in updating the θ parameters were investigated. By selecting specific test functions, the advantages and disadvantages of each approach are compared with each other in terms of the number of oscillations, the parameter update rate and the minimum cost reached. The comparison results are shown graphically.

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps that lead to rank decreases, maintaining low-rank solutions throughout the algorithm. Moreover, the optimization problems are constrained to ensure that the rank-drop step is also feasible and can be readily incorporated into a projection-free minimization method, e.g., Frank-Wolfe. We demonstrate that by incorporating rank-drop steps into the Frank-Wolfe algorithm, the rank of the solution is greatly reduced compared to the original Frank-Wolfe or its common variants.

While the line-search-based method of Chapter 10 is quick and easy to understand, it does not exploit the full power of a model function. In essence, the model-based descent algorithm for unconstrained optimization only uses gradient approximations to confirm descent directions. This can be seen in the convergence analysis of Chapter 10, where only controllably accurate gradient approximations are used. In particular, convergence does not even require that the function values f(x k ) be estimated by a model.

Through this book, and in all areas of optimization, it should always be remembered that whenever derivatives are available, they should be used. Derivatives, or more generally gradients, provide powerful information about a function. In unconstrained optimization, descent directions and first order optimality hinge on these basic objects of multivariate calculus. Hessian matrices provide extremely powerful information regarding the local curvature of a function, and can be employed to build quadratically convergent algorithms.

In the work there is considered an NP-hard flexible job shop problem. Its solution lies in allocation of operations to machines and determination of the sequence of their execution. There is also a method of construction of approximate algorithms presented, based on the idea of descent search, determining the allocation of operations. What is more, there were computational experiments conducted to investigate the correlation between the size of the neighborhood and the quality of solutions determined by the algorithm.

Differences between the gradient-based search methods and direct search methods are explained. This chapter focuses on the gradient-based unconstrained search methods. General concepts related to iterative numerical algorithms are presented and discussed. These basic concepts are applicable to both unconstrained and constrained optimization problems. The ideas of a descent direction and descent step for unconstrained minimization are presented, discussed and illustrated. Each algorithm has two fundamental steps: search direction determination and step size calculation. The step size calculation along a search direction is posed as a one-dimensional minimization problem. An analytical method to compute step size and interval-reducing numerical methods for step size calculation are presented. The prominent method in this class is the golden sections method. The steepest descent method for search direction determination is detailed and illustrated. The conjugate gradient method is described as a minor modification of the steepest descent method and illustrated in an example. Two other conjugate gradient methods are also presented.

In order to determine valid production results in the area of NC-based tooling machine, complex simulation tools are used. The challenge is the calculation of the material removal, tool paths as well as valid setup positions of workpiece and periphery which leads mostly to high computational time. The descent of the computational effort includes a high portion of systems engineering. This contribution shows a theoretical concept to substitute complex simulation models by calculation models which observes the inverse kinematic behavior of the machine in combination with a NC-parser which estimates valid workpiece positions. The contribution compares model approaches of inverse kinematic problems considering 5 axis tooling machine to determine valid setup positions and minimize theoretical calculation effort.

Model-based methods in DFO proceed from the idea that if it is possible to build a “good” model of the true objective function, then information from the model can be used to guide the optimization. In Chapter 9, we studied several methods for constructing model functions using only objective function evaluations. We also defined fully linear, as a term to mean that the optimiser has access to an accuracy parameter \(\Delta \) that can be used to drive the error in the model to 0 in a predictable way. We now turn our attention to how to employ model functions in unconstrained DFO algorithms.

Realizing the pinpoint landing localization for the ChangE-3 system is a symbol of success for this mission, and it is also a basic requirement for the lunar Lander and Rover to carry out the following scientific exploration tasks. In this paper, jointly dealing with the descent image sequence and ChangE-2 DOM data, an approach based on the images processing techniques, such as SIFT feature matching, homography transportation and stereo vision measurement, is presented to realize the pinpoint localization of the ChangE-3 system. The localization result is proved to be reliable and accuracy and the result will be a critical component for the ChangE-3 mission planning and the completion of scientific exploration.

In this letter, a hybrid descent method is used to determine a set of filter parameters for a sigmoid filter which attempts to work under various SNR conditions. It overcomes the limitations of the current sigmoid filters that performs effectively only at a single SNR. Results show that significant improvement in terms of better speech qualities can be achieved by the proposed sigmoid filter when working under various SNR conditions.

This paper develops two implementations of Halpern-type proximal algorithms (HPA1 and HPA2) solving nonsmooth problems. We prove their convergence to the solutions of the problems under the new conditions. Applying this idea to the Basis Pursuit model in image/signal processing, a new Halpern-type proximal algorithm (HPA) for the model is obtained. Experiments show that the Halpern-type proximal algorithm has better descent property than the usual proximal algorithm (PA) for the Basis Pursuit model.

International audience; Sparsity-inducing penalties are useful tools in variational methods for machine learning. In this paper, we propose two block-coordinate descent strategies for learning a sparse multiclass support vector machine. The first one works by selecting a subset of features to be updated at each iteration, while the second one performs the selection among the training samples. These algorithms can be efficiently implemented thanks to the flexibility offered by recent randomized primal-dual proximal methods. Experiments carried out for the supervised classification of handwritten digits demonstrate the interest of considering the primal-dual approach in the context of block-coordinate descent, and the efficiency of the proposed algorithms is assessed through a comparison of execution times and classification errors. Index Terms— Sparsity, multiclass SVM, proximal algorithm, random update, block-coordinate descent.

We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive interpretation to the latter algorithm. We show that a new algorithm, which we term Regularised Gradient Descent, can converge more quickly than either Nesterov's algorithm or the classical momentum algorithm.

International audience; The NP-hard capacitated clustering problem (CCP) is a general model with a number of relevant applications. This paper proposes a highly effective iterated variable neighborhood search (IVNS) algorithm for solving the problem. IVNS combines an extended variable neighborhood descent method and a randomized shake procedure to explore effectively the search space. The computational results obtained on three sets of 133 benchmarks reveal that the proposed algorithm competes favorably with the state-of-the-art algorithms in the literature both in terms of solution quality and computational efficiency. In particular, IVNS discovers an improved best known result (new lower bounds) for 28 out of 83 most popular instances, while matching the current best known results for the remaining 55 instances. Several essential components of the proposed algorithm are investigated to understand their impacts on the performance of algorithm.

Algebraic Set Theory, a reconsideration of Zermelo-Fraenkel set theory (zfc) in category-theoretic terms, has been built up in the mid-nineties by Andre Joyal and Ieke Moerdijk. Since then, it has developed into a whole research program. This paper gets back to the original formulation by Joyal and Moerdijk, and more specifically to its first three axioms. It explains in detail that these axioms set up a framework directly linked to descent theory, a theory having to do with the shift from local data to a global item in modern algebraic geometry. Fibered categories, introduced by Grothendieck, provide a powerful framework for descent theory: They formalize in a very general way the consideration of local data of different kinds over the objects of some base category. The paper shows that fibered categories fit Joyal and Moerdijk’s axiomatization in a natural way, since the latter actually aims to secure a descent condition. As a result, Algebraic Set Theory is shown to accomplish, not only an original and fruitful combination of set theory with category theory, but the genuine graft of a deeply geometric idea onto the usual setting of zfc.

In this work we address the inverse problem of reconstructing inclusions and their thermal parameters given temperature measurements at the accessible side of a material. We describe an iterative descent method that combines topological derivative computations to reconstruct the geometry of the defects with gradient iterations to approximate the material parameters. A numerical experiment showing the ability of the method to obtain reasonable reconstructions in a few iterations is presented.