Related papers: Geometric Programming for Optimal Positive Linear …
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
The gradient mapping norm is a strong and easily verifiable stopping criterion for first-order methods on composite problems. When the objective exhibits the quadratic growth property, the gradient mapping norm minimization problem can be…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
In this paper, we present a new geometric approach for sensitivity analysis in linear programming that is computationally practical for a decision-maker to study the behavior of the optimal solution of the linear programming problem under…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear…
Automatic parameter tuning methods for planning algorithms, which integrate pipeline approaches with learning-based techniques, are regarded as promising due to their stability and capability to handle highly constrained environments. While…