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The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of…
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
This article presents a discussion of optimization problems where the objective function f(x) has parameters that are constrained by some scaling, so that q(x) = constant, where this function q() involves a sum of the parameters, their…
This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxations are used to solve the sample average optimization.…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…
Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…