Related papers: Combining Convex-Concave Decompositions and Linear…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…
Convex optimization with feedback is a framework where a learner relies on iterative queries and feedback to arrive at the minimizer of a convex function. It has gained considerable popularity thanks to its scalability in large-scale…
We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
We address the problem of linear precoder (beamformer) design in a multiple-input multiple-output interference channel (MIMO-IC). The aim is to design the transmit covariance matrices in order to achieve max-min utility fairness for all…
We introduce a new convexified matching method for missing value imputation and individualized inference inspired by computational optimal transport. Our method integrates favorable features from mainstream imputation approaches: optimal…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…
We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis,…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Input design is an important issue for classical system identification methods but has not been investigated for the kernel-based regularization method (KRM) until very recently. In this paper, we consider in the time domain the input…