Related papers: Parametric Nonconvex Optimization via Convex Surro…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
The central task in modeling complex dynamical systems is parameter estimation. This task involves numerous evaluations of a computationally expensive objective function. Surrogate-based optimization introduces a computationally efficient…
Evaluation metrics in machine learning are often hardly taken as loss functions, as they could be non-differentiable and non-decomposable, e.g., average precision and F1 score. This paper aims to address this problem by revisiting the…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
A surrogate function is often employed to reduce the number of objective function evaluations for optimization. However, the effect of using a surrogate model in evolutionary approaches has not been theoretically investigated. This paper…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this…
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…
Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
In this work we provide a theoretical framework for structured prediction that generalizes the existing theory of surrogate methods for binary and multiclass classification based on estimating conditional probabilities with smooth convex…