Related papers: On Substochastic Inverse Eigenvalue Problems with …
We study the inverse eigenvalue problem for finding doubly stochastic matrices with specified eigenvalues. By making use of a combination of Dykstra's algorithm and an alternating projection process onto a non-convex set, we derive hybrid…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…
We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation…
We consider a stochastic Inverse Variational Inequality (IVI) problem defined by a continuous and co-coercive map over a closed and convex set. Motivated by the absence of performance guarantees for stochastic IVI, we present a…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Stochastic Optimal Control Problems (SOCPs) plays a major role in the sequential decision-making challenges. There exist various iterative algorithms, under framework of stochastic maximum principle, that sequentially find the optimal…
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
Many real-world problems, such as those with fairness constraints, involve complex expectation constraints and large datasets, necessitating the design of efficient stochastic methods to solve them. Most existing research focuses on cases…
We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalue Problem (SNIEP) is the problem of characterising all…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…
The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks which sets of numbers (counting multiplicities) can be the eigenvalues of a symmetric matrix with nonnegative entries. While examples of such matrices are abundant in linear…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…