We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging barriers. For the purpose, we first show how error bounds may be constructed using objects called one-step facial … Read more
The ” fast iterative shrinkage-thresholding algorithm ” (FISTA) is one of the most famous first order optimization scheme, and the stepsize, which plays an important role in theoretical analysis and numerical experiment, is always determined by a constant related to the Lipschitz constant or by a backtracking strategy. In this paper, we design a new … Read more
We consider polyhedral separation of sets as a possible tool in supervised classification. In particular we focus on the optimization model introduced by Astorino and Gaudioso and adopt its reformulation in Difference of Convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of … Read more
We present conditions for Hölder calmness and upper Hölder continuity of optimal solution sets to perturbed optimization problems in finite dimensions. Studies on Hölder type stability were a popular subject in variational analysis already in the 1980ies and 1990ies, and have become a revived interest in the last decade. In this paper, we focus on … Read more
We investigate optimization problems with a non-smooth partial differential equation as constraint, where the non-smoothness is assumed to be caused by Nemytzkii operators generated by the functions abs, min and max. For the efficient as well as robust solution of such problems, we propose a new optimization method based on abs-linearization, i.e., a special handling … Read more
In this paper, we investigate the Moreau envelope of the supremum of a family of convex, proper, and lower semicontinuous functions. Under mild assumptions, we prove that the Moreau envelope of a supremum is the supremum of Moreau envelopes, which allows us to approximate possibly nonsmooth supremum functions by smooth functions that are also the … Read more
For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact proximal-Newton-type methods, or successive quadratic approximation (SQA) methods, are widely used for their superlinear convergence in terms of iterations. However, unlike the counter parts in smooth optimization, they suffer from lengthy running time in solving regularized … Read more
Block tridiagonal systems appear in classic Kalman smoothing problems, as well in generalized Kalman smoothing, where problems may have nonsmooth terms, singular covariance, constraints, nonlinear models, and unknown parameters. In this paper, first we interpret all the classic smoothing algorithms as different approaches to solve positive definite block tridiagonal linear systems. Then, we obtain new … Read more
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation – transforming the original problem into a constrained problem in a higher dimensional space – to define a sequence of suitable quadratic penalty subproblems with increasing penalty … Read more
We present a decentralized failure-tolerant algorithm for optimizing electric vehicle (EV) charging, using charging stations as computing agents. The algorithm is based on the alternating direction method of multipliers (ADMM) and it has the following features: (i) It handles capacity, peak demand, and ancillary services coupling constraints. (ii) It does not require a central agent … Read more