Convergence of a distributed method for minimizing sum of convex functions with fixed point constraints

In this paper, we consider a distributed optimization problem of minimizing sum of convex functions over the intersection of fixed-point constraints. We propose a distributed method for solving the problem. We prove the convergence of the generated sequence to the solution of the problem under certain assumption. We further discuss the convergence rate with an appropriate positive stepsize. A numerical experiment is given to show the effectiveness of the obtained theoretical result.

A note on no-free-lunch theorem

The No-Free-Lunch theorem is an interesting and important theoretical result in machine learning. Based on philosophy of No-Free-Lunch theorem, we discuss extensively on the limitation of a data-driven approach in solving NP-hard problems.

Near-Epoch Dependence

Near‐epoch dependence (NED) is a generalized dependence concept for functions of mixing processes. This chapter gives definitions and examples, and considers the application to nonlinear dynamic processes. The relation to mixingales is the key theoretical result. Results on the preservation of NED under various transformations and a special result for the adapted sequence case are considered next. Finally, the related concept of approximability is defined which, unlike NED, can hold in the absence of integer moments.

Estimación de la Eficiencia de una Hélice Operando en Régimen Compresible Subsónico

La información experimental disponible para hélices no es útil cuando el número de Mach de la punta de la pala es mayor a . Con el fin de verificar esta aseveración, se propuso un caso de estudio para una hélice Navy 5868-9 con perfil aerodinámico Clark-Y de 4 palas operando a un número de Mach de avance de 0.59 y un número de Mach en la punta de la pala de 0.95. La eficiencia experimental de la hélice (obtenida de gráficas) se compara con la eficiencia obtenida empleando la teoría combinada y con la eficiencia obtenida al corregir la teoría combinada por efectos de compresibilidad con la metodología propuesta en este trabajo. Se concluye que la información experimental disponible para hélices no es adecuada cuando el número de Mach en la punta de la pala es mayor que el Mach crítico, siendo más conveniente el resultado teórico corregido por compresibilidad. The experimental information available for propellers is not useful when the Mach number of the tip of the blade is greater than 0.3. In order to verify this assertion, a case study was proposed for a Navy propeller 5868-9 with a 4-blade Clark-Y airfoil section operating at an advance Mach number of 0.59 and a Mach number at the tip of the blade of 0.95. The experimental efficiency of the propeller (obtained from graphs) is compared with the efficiency obtained using the combined theory and with the efficiency obtained by correcting the combined theory for compressibility effects with the methodology proposed in this paper. It is concluded that the experimental information available for propellers is not suitable when the Mach number at the tip of the blade is greater than the critical Mach, being more convenient the theoretical result corrected by compressibility.

The Effect of Different Scale on Object to the Approximation of the First Order Polarization Tensor of Sphere, Ellipsoid, and Cube

Polarization tensor (PT) is a classical terminology in fluid mechanics and theory of electricity that can describe geometry in a specific boundary domain with different conductivity contrasts. In this regard, the geometry may appear in a different size, and for easy characterizing, the usage of PT to identify particular objects is crucial. Hence, in this paper, the first order polarization tensor for different types of object with a diverse range of sizes are presented. Here, we used three different geometries: sphere, ellipsoid, and cube, with fixed conductivity for each object. The software Matlab and Netgen Mesh Generator are the essential mathematical tools to aid the computation of the polarization tensor. From the analytical results obtained, the first order PT for sphere and ellipsoid depends on the size of both geometries. On the other hand, the numerical investigation is conducted for the first order PT for cube, since there is no analytical solution for the first order PT related to this geometry, to further verify the scaling property of the first order PT due to the scaling on the size of the original related object. Our results agree with the previous theoretical result that the first order polarization tensor of any geometry will be scaled at a fixed scaling factor according to the scaling on the size of the original geometry.

Multiple Solutions for Some Classes Integro-Dynamic Equations on Time Scales

In this chapter we study a class of second-order integro-dynamic equations on time scales. A new topological approach is applied to prove the existence of at least two non-negative solutions. The arguments are based upon a recent theoretical result.

Decentralized Decisions and Technological Progress: A Formal Proof

This paper provides attempts to formalize Hayek’s theory of knowledge. It has been theoretically shown that exponential income distribution is a spontaneous order of the well-functioning market economy. We show that this theoretical result is supported by the empirical evidence from the United Kingdom and China. In particular, we empirically show how the income structure of China evolved towards an exponential distribution after the market-oriented economic reformation. Furthermore, we strictly prove that, if the income structure of an economy obeys an exponential distribution, the income summation over all households leads to an aggregate production function with Hicks-neutral-like technical progress, in which the technology factor is exactly equal to society’s information stock that is a result of combining all of decentralized decisions.

Synchronization in complete networks of reaction-diffusion equations of FitzHugh-Nagumo type with nonlinear coupling

The synchronization in complete network consisting of nodes is studied in this paper. Each node is connected to all other ones by nonlinear coupling and is represented by a reaction-diffusion system of FitzHugh-Nagumo type which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, the sufficient condition on the coupling strength to achieve the synchronization is found. The result shows that the networks with bigger in-degrees of nodes synchronize more easily. The paper also presents the numerical simulations for theoretical result and shows a compromise between the theoretical and numerical results.

A conjecture on a continuous optimization model for the Golomb Ruler Problem

A Golomb Ruler (GR) is a set of integer marks along an imaginary ruler such that all the distances of the marks are different. Computing a GR of minimum length is associated to many applications (from astronomy to information theory). Although not yet demonstrated to be NP-hard, the problem is computationally very challenging. This brief note proposes a new continuous optimization model for the problem and, based on a given theoretical result and some computational experiments, we conjecture that an optimal solution of this model is also a solution to an associated GR of minimum length.

Decision Tools Regarding Time Constraints Violation in Manufacturing Workshops

This paper is dedicated to the study of constraints violation in manufacturing workshops with time constraints. In such systems, every operation duration is included between minimal and maximal values. P-time Petri nets are used for modeling. A new theorem is introduced, constituting a decision tool about the occurrence of constraints violation at the level of a synchronization transition when various types of time disturbances occur. It shows the robustness properties of a manufacturing system on a range that may include delay and advance disturbances. The theoretical result is illustrated step by step on a given workshop. Two other lemmas are elaborated contributing to the study of the constraints violation problem. The final goal is to generalize the robustness property towards simultaneous occurrence of two delays at two points of the system, each having its own robustness range.