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This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's…
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration…
We propose a subgradient-based method for finding the maximum feasible subsystem in a collection of closed sets with respect to a given closed set $C$ (MFS$_C$). In this method, we reformulate the MFS$_C$ problem as an $\ell_0$ optimization…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…