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Convex Analysisの二,三の進展について

On robust estimation of the location parameter

Introduction to stochastic programming

Convex Analysis: (pms-28)

We present a general purpose solver for quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix in each iteration. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. It is division-free once an initial matrix factorization is carried out, making it suitable for real-time applications in embedded systems. In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The method also supports factorization caching and warm starting, making it particularly efficient when solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint, is library-free, and has been extensively tested on many problem instances from a wide variety of application areas. It is typically ten times faster than competing interior point methods, and sometimes much more when factorization caching or warm start is used.

OSQP: An Operator Splitting Solver for Quadratic Programs

We consider the problem of learning discounted-cost optimal control policies for unknown deterministic discrete-time systems with continuous state and action spaces. We show that a policy evaluation step of the well-known policy iteration (PI) algorithm can be characterized as a solution to an infinite dimensional linear program (LP). However, when approximating such an LP with a finite dimensional program, the PI algorithm loses its nominal properties. We propose a data-driven PI scheme that ensures a certain monotonic behavior and allows for incorporation of expert knowledge on the system. A numerical example illustrates effectiveness of the proposed algorithm.

A Data-Driven Policy Iteration Scheme based on Linear Programming

In this paper, we consider the regularized version of the Jacobi algorithm, a block coordinate descent method for convex optimization with an objective function consisting of the sum of a differentiable function and a block-separable function. Under certain regularity assumptions on the objective function, this algorithm has been shown to satisfy the so-called sufficient decrease condition, and consequently, to converge in objective function value. In this paper, we revisit the convergence analysis of the regularized Jacobi algorithm and show that it also converges in iterates under very mild conditions on the objective function. Moreover, we establish conditions under which the algorithm achieves a linear convergence rate.

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On the Convergence of a Regularized Jacobi Algorithm for Convex Optimization

We consider a resource allocation problem over an undirected network of agents, where edges of the network define communication links. The goal is to minimize the sum of agent-specific convex objective functions, while the agents' decisions are coupled via a convex conic constraint. We derive two methods by applying the alternating direction method of multipliers (ADMM) for decentralized consensus optimization to the dual of our resource allocation problem. Both methods are fully parallelizable and decentralized in the sense that each agent exchanges information only with its neighbors in the network and requires only its own data for updating its decision. We prove convergence of the proposed methods and demonstrate their effectiveness with a numerical example.

Decentralized Resource Allocation via Dual Consensus ADMM

https://cyberleninka.org/article/n/1019414.pdf

Dynamic Day-ahead Water Pricing Based on Smart Metering and Demand Prediction

In this work, identification of 24-hours-ahead water demand prediction model based on historical water demand data is considered. As part of the identification procedure, the input variable selection algorithm based on partial mutual information is implemented. It is shown that meteorological data on a daily basis are not relevant for the water demand prediction in the sense of partial mutual information for the analysed water distribution systems of the cities of Tavira, Algarve, Portugal and Evanton East, Scotland, UK. Water demand prediction system is modelled using artificial neural networks, which offer a great potential for the identification of complex dynamic systems. The adaptive tuning procedure of model parameters is also developed in order to enable the model to adapt to changes in the system. A significant improvement of the prediction ability of such a model in relation to the model with fixed parameters is shown when a certain trend is present in the water demand profile.

Goran Banjac

Papers

A Data-Driven Policy Iteration Scheme based on Linear Programming

On the Convergence of a Regularized Jacobi Algorithm for Convex Optimization

Decentralized Resource Allocation via Dual Consensus ADMM

Dynamic Day-ahead Water Pricing Based on Smart Metering and Demand Prediction

Adaptable urban water demand prediction system