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Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
Matrix geometric means between two positive definite matrices can be defined from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system…
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…
Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue…
We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an $L^2$ neighborhood of a local solution that satisfies no-gap second-order sufficient…
We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result,…
In practical engineering and optimization, solving multi-objective optimization (MOO) problems typically involves scalarization methods that convert a multi-objective problem into a single-objective one. While effective, these methods often…
In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation,…