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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…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…
The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the…
We study convergence rates of the classic proximal bundle method for a variety of nonsmooth convex optimization problems. We show that, without any modification, this algorithm adapts to converge faster in the presence of smoothness or a…
In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally Lipschitz differentiable (possibly nonconvex) function,…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Decades of advances in mixed-integer linear programming (MILP) and recent development in mixed-integer second-order-cone programming (MISOCP) have translated very mildly to progresses in global solving nonconvex mixed-integer quadratically…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem…