Related papers: Avoiding Traps in Nonconvex Problems
Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
The last decade witnessed a rise in the importance of supervised learning applications involving {\em big data} and {\em big models}. Big data refers to situations where the amounts of training data available and needed causes difficulties…
The online meta-learning framework is designed for the continual lifelong learning setting. It bridges two fields: meta-learning which tries to extract prior knowledge from past tasks for fast learning of future tasks, and online-learning…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
Self-concordant barriers are essential for interior-point algorithms in conic programming. To speed up the convergence it is of interest to find a barrier with the lowest possible parameter for a given cone. The barrier parameter is a…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Regression in supervised learning often requires the enforcement of constraints to ensure that the trained models are consistent with the underlying structures of the input and output data. This paper presents an iterative procedure to…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple…
In this work we propose a Model Predictive Control (MPC) formulation that splits constraints in two different types. Motivated by safety considerations, the first type of constraint enforces a control-invariant set, while the second type…
Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert…
This work presents a new method for online selection of multiple penalty parameters for the alternating direction method of multipliers (ADMM) algorithm applied to optimization problems with multiple constraints or functionals with block…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
We consider the problem of computationally-efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…