Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
This paper introduces the class of weakly quasar-convex functions, a notion that simultaneously generalizes weak convexity (and hence convexity) and quasar-convexity. We establish the theoretical foundation for this new class by developing its basic calculus, deriving characterizations, and systematically investigating its closure and structural properties. Building on these tools, we analyze the proximal point algorithm … Read more
In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved inexactly using stochastic second-order methods. We establish iteration complexity results for obtaining approximate second-order stationary … Read more
In this paper, we propose new inexact adaptive proximal gradient algorithms for solving nonconvex composite optimization problems, where the objective is the sum of a differentiable nonconvex function and a convex non-differentiable function. A new relative error criterion to compute the proximal operator inexactly has been proposed together with new adaptive strate- gies for selecting … Read more
This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more
This paper studies geometric and structural properties of quadratic multiobjective optimization problems. Thereby, a multiobjective optimization problem is called convexlike if the upper image, i.e., the image set plus the nonnegative orthant, is a convex set. Moreover, we say that a feasible point is supported in case it is a minimal solution of a weighted … Read more
A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (OFFO) methods, and it is based on the AdaGrad algorithm. At each iteration, our method computes an adaptive step size based on the cumulative sum of block gradients, instead … Read more
We present PyROS, a Python-based meta-solver that automates a generalized cutting-set algorithm for the solution of nonconvex two-stage robust optimization (RO) problems with uncertain equality constraints. Freely available through the open-source optimization software package Pyomo, PyROS is designed to operate on a user-provided deterministic model and uncertainty set, such that a solution to the RO … Read more
We propose and analyze an inexact proximal point method for minimizing locally Lipschitz functions on Euclidean spaces with a piecewise star-convex structure. More precisely, the space is covered by finitely many closed convex sets, and on each set the objective function satisfies a star-convex inequality with respect to the minimizers of its restriction. This class … Read more
In this paper we develop and implement sequential nonlinear-programming methods for solving the thermal-aware soft-macro VLSI floorplanning problem with IO-block placement and a dynamic floorplan-boundary. We develop a multi-stage nonlinear-programming approach to this floorplanning problem. We break the floorplanning process into two main stages, a simplified first-stage, which omits any consideration of the floorplan boundary … Read more