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Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
This paper proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the average of…
When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU-intensive, and are useless on untractable NP-hard problems that would require thousands of…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the…
In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents' local functions by performing a combination of local gradient evaluations and…
The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
Dynamic optimization of mean and variance in Markov decision processes (MDPs) is a long-standing challenge caused by the failure of dynamic programming. In this paper, we propose a new approach to find the globally optimal policy for…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
We consider the consensual distributed optimization problem in the Riemannian context. Specifically, the minimization of a sum of functions form is studied where each individual function in the sum is located at the node of a network. An…
Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…