Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original row sparsity and row sparsity pattern. However, the confidence-constrained opt...

based on credibilistic value-at-risk (cvar) of regularfuzzy variable, we introduce a new cvar reduction method fortype-2 fuzzy variables. the reduced fuzzy variables arecharacterized by parametric possibility distributions. we establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. the convex properties of second order moments with ...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

Large-margin structured estimation methods work by minimizing a convex upper bound of loss functions. While they allow for efficient optimization algorithms, these convex formulations are not tight and sacrifice the ability to accurately model the true loss. We present tighter non-convex bounds based on generalizing the notion of a ramp loss from binary classification to structured estimation. ...

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in ...

We propose a novel method to find approximate convex 3D shapes from single RGBD images. Convex shapes are more general than cuboids, cylinders, cones and spheres. Many real-world objects are nearconvex and every non-convex object can be represented using convex parts. By finding approximate convex shapes in RGBD images, we extract important structures of a scene. From a large set of candidates ...

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs ...

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate method, which alternates between maximizing over one (or more) randomly chosen dual variable and minimizing over the primal variab...

in this paper, we describe our implementation of an interior point algorithm for large scale systems. first we identify system with small and medium methods convex optimization, then we use interior point method for identification. finally we offer an interior point method that uses nonlinear cost function and see that we achieve a good trade-off between error and cpu time. actually, in this pa...

This paper studies a joint optimization problem of sub-carrier assignment and power allocation in orthogonal frequency division multiple access (OFDMA) wireless networks. A major challenge in solving the optimization problem is non-convexity caused by the combinatorial nature of sub-carrier assignment problem and/or non-convex objective functions. To address the combinatorial complexity, we for...