The formulation min f(x)+g(y) subject to Ax+By=b, where f and g are extended-value convex functions, arises in many application areas such as signal processing, imaging and image processing, statistics, and machine learning either naturally or after variable splitting. In many common problems, one of the two objective functions is strictly convex and has Lipschitz continuous … Read more
In multi-objective optimization the objective is to reach a point which is Pareto ecient. However we usually encounter many such points and choosing a point amongst them possesses another problem. In many applications we are required to choose a point having a good spread over all objective functions which is a direct consequence of the … Read more
We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after O(n) iterations with overall arithmetic complexity O(n²). Numerical experiments show that in practice the method converges in a small number of iterations with overall linear complexity, … Read more
In this paper we argue for aggregated models in decomposition schemes for two-stage stochastic programming problems. We observe that analogous schemes proved effective for single-stage risk-averse problems, and for general linear programming problems. A major drawback of the aggregated approach for two-stage problems is that an aggregated master problem can not contain all the information … Read more
Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each … Read more
In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive sensing, recent work has used random Toeplitz and circulant sensing matrices and proved their efficiency in theory, by computer simulations, as well as through physical … Read more
This paper considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. We review some of its interesting examples and propose a generalized block coordinate descent method. (Using proximal updates, we further allow non-convexity over some blocks.) Under certain conditions, we show that … Read more
This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from both viewpoints of optimization theory and its applications. Based on second- order generalized differential tools of variational analysis, we obtain … Read more
In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized smoothing equation for NCP with generalized monotonicity. Our results provide a theoretical basis to develop a new computational method for nonlinear equation systems … Read more
We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving a convex linear programming (LP) problem over the … Read more