Related papers: On approximate quasi Pareto solutions in nonsmooth…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute),…
Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
In this paper, we extend the class of strongly $E$-preinvex and strongly $E$-invex functions to quasi strongly $E$-preinvex, quasi strongly $E$-invex and pseudo strongly $E$-invex functions. Some nontrivial suitable examples have been…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the…
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint sets. The main attention is paid to the two major…
In this article, we view the approximate version of Pareto and weak Pareto solutions of the multiobjective optimization problem through the lens of KKT type conditions. We also focus on an improved version of Geoffrion proper Pareto…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…