All posts under category "Mathematics / Math.OC"
A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle high-dimensional global optimisation problems, and it has been successfull
There is a considerable amount of ongoing research on the use of Bayesian control charts for detecting a shift from a good quality distribution to a bad quality distribution in univariate and multivariate processes. It is widely claimed that Bayesian control charts are economically optimal; see, for
We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of them contains all tridiagonal P-matrices.
ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab and when n = N, ML(N)BiCGStab is GMRES/FOM where N is the si
The history of structural optimization as an exact science begins possibly with the celebrated Lagrange problem: to find a curve which by its revolution about an axis in its plane determines the rod of greatest efficiency. The Lagrange hypothesis, that the optimal rod possesses the constant cross-se
In this article three models of firms interaction on the market are described. One of these models is described by using a differential equation and by Lotka-Volterra model, where the equation has a different form. Also, there are models of non-competing and competing firms. The article presents an
The kissing number in n-dimensional Euclidean space is the maximal number of non-overlapping unit spheres which simultaneously can touch a central unit sphere. Bachoc and Vallentin developed a method to find upper bounds for the kissing number based on semidefinite programming. This paper is a repor
In this note we contrast two transformation-based methods to deduce absolute extrema and the corresponding extremizers. Unlike variation-based methods, the transformation-based ones of Carlson and Leitmann and the recent one of Silva and Torres are direct in that they permit obtaining solutions by i
We analyze independent policy-gradient (PG) learning in $N$-player linear-quadratic (LQ) stochastic differential games. Each player employs a distributed policy that depends only on its own state and updates the policy independently using the gradient of its own objective. We establish global linear
We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to 'intelligent' PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varyin
Over the past decade, several researchers have presented various optimisation algorithms for use in truss design. The no free lunch theorem implies that no optimisation algorithm fits all problems; therefore, the interest is not only in the accuracy and convergence rate of the algorithm but also the
We consider the four-dimensional nonholonomic distribution defined by the 4-potential of the electromagnetic field on the manifold. This distribution has a metric tensor with the Lorentzian signature $(+,-,-,-)$, therefore, the causal structure appears as in the general relativity theory. By means o
The paper studies decentralized optimization over networks, where agents minimize a sum of {it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {it adaptively} adjust their stepsize via local backtracking proced
Developing effective control strategies for behind-the-meter energy storage to coordinate peak shaving and stacked services is essential for reducing electricity costs and extending battery lifetime in commercial buildings. This work proposes an end-to-end, two-stage framework for coordinating peak
We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process model, and past evaluation results. The main difficulty with th
In many applications, nodes in a network desire not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This paper shows that, for the scalar case and by assuming a bit more, novel non-gradien
This brief presents a simple derivation of the standard model-free control for the non-minimum phase systems. The robustness of the proposed method is studied in simulation considering the case of switched systems.
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to the minimizer of the energy function under consideration, an
The question tackled here is the time allocation of radars in a multitarget environment. At a given time radars can only observe a limited part of the space; it is therefore necessary to move their axis with respect to time, in order to be able to explore the overall space facing them. Such sensors
This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions. Existence of generalized solutions is established via a hybrid a
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled process can not be observed, and at any time the control action
We survey a new paradigm in signal processing known as 'compressive sensing'. Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately
This document consists of two parts: the second part was submitted earlier as a new proof of Nash's theorem, and the first part is a note explaining a problem found in that proof. We are indebted to Sergiu Hart and Eran Shmaya for their careful study which led to their simultaneous discovery of this
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze na
The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm for the multidimensional knapsack problem with Java and C++ cod
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory, from its roots in the calculus of variations and the classical theory of control to the present time, giving particular
There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifications given
A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method is proved to have certain de
In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presen
With the increasing of electric vehicle (EV) adoption in recent years, the impact of EV charging activities to the power grid becomes more and more significant. In this article, an optimal scheduling algorithm which combines smart EV charging and V2G gird service is developed to integrate EVs into p
We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately. Current
We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are o
Ant Colony System (ACS) is a distributed (agent- based) algorithm which has been widely studied on the Symmetric Travelling Salesman Problem (TSP). The optimum parameters for this algorithm have to be found by trial and error. We use a Particle Swarm Optimization algorithm (PSO) to optimize the ACS
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the sa
We obtain the functional defining the price and quality of sample readings of the generalized velocities. It is shown that the optimal sampling frequency, in the sense of minimizing the functional quality and price depends on the sampling of the upper cutoff frequency of the analog signal of the ord
We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in its neighborhood. We introduce a topological property known
We consider the symmetric rendezvous search game on a complete graph of n locations. In 1990, Anderson and Weber proposed a strategy in which, over successive blocks of n-1 steps, the players independently choose either to stay at their initial location or to tour the other n-1 locations, with proba
We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it
Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally mul
We consider an example by Haviv (1996) of a constrained Markov decision process that, in some sense, violates Bellman's principle. We resolve this issue by showing how to preserve a form of Bellman's principle that accounts for a change of constraint at states that are reachable from the initial sta
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two tangentially convex (DTC) functions. More precisely, we develop a ra
In this paper, we examine higher order difference problems. Using the 'squeezing' argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, two needed assumptions are identified. A counterexample, in which the transversality condition is not
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in cite{nos} for the infinite horizon case to the finite horizon case. We prove an a priori bound of size $O(h+k)$ for the method, $h$ being the
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal' + ``first-order dual'' continuous-time dynamical system, in which both the
The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or absence of an intruder nearby. The detection of the transiti
In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic linfty-norm performance-loss bounds for DPP in the presence of approximat
The spaces D, S and E' over mathbb{R}^(n) are known to be flat modules over A=mathbb{C}[partial_{1},...,partial_{n}], whereas their duals D', S' and E are known to be injective modules over the same ring. Let A be a Noetherian k-algebra (k=mathbb{R} or mathbb{C}). The above observation leads us to s
The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature do not minimize directly the settling time bu
The projection algorithm is frequently used in adaptive control and this note presents a detailed analysis of its properties.
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control
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