Related papers: A Fast Eigenvalue Approach for Solving the Trust R…
In this paper, we study the maximization problem of the second non-zero Laplace eigenvalue $\lambda_2(T,g)$ on a torus $T$, among all unit-area metrics in a fixed conformal class. First, we obtain a new upper bound for…
We consider optimal control problems that have binary-valued control input functions and a perimeter regularization. We develop and analyze a trust-region algorithm that solves a sequence of subproblems in which the regularization term and…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…
In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced…
This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
We seek to impose linear, equality constraints in feedforward neural networks. As top layer predictors are usually nonlinear, this is a difficult task if we seek to deploy standard convex optimization methods and strong duality. To overcome…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…
Utility-based shortfall risk (UBSR), a convex risk measure sensitive to tail losses, has gained popularity in recent years. However, research on computational methods for UBSR optimization remains relatively scarce. In this paper, we…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…