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We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Recent results in homotopy and solution paths demonstrate that certain well-designed greedy algorithms, with a range of values of the algorithmic parameter, can provide solution paths to a sequence of convex optimization problems. On the…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…
We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical…
We describe a combinatorial algorithm which, given a monotone and consistent symmetric set function d on a finite set V in the sense of Rizzi, constructs a non trivial set S minimizing d(S,V-S). This includes the possibility for the…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
Distributed computing frameworks such as MapReduce are often used to process large computational jobs. They operate by partitioning each job into smaller tasks executed on different servers. The servers also need to exchange intermediate…
Machine learning workflow development is a process of trial-and-error: developers iterate on workflows by testing out small modifications until the desired accuracy is achieved. Unfortunately, existing machine learning systems focus…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
Many decision-making algorithms draw inspiration from the inner workings of individual biological systems. However, it remains unclear whether collective behavior among biological species can also lead to solutions for computational tasks.…
Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems, like Dominating Set and Independent Set. In this paper, we propose to use measure and conquer also as a tool in the…