Related papers: Minimizing a Sum of Clipped Convex Functions

We describe general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a nonconvex set. The heuristics, which employ convex relaxations, convex restrictions, local neighbor search…

We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…

The problem of minimizing sum-of-nonconvex functions (i.e., convex functions that are average of non-convex ones) is becoming increasingly important in machine learning, and is the core machinery for PCA, SVD, regularized Newton's method,…

In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…

This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model…

We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…

We consider in this paper a class of semi-continuous quadratic programming problems which arises in many real-world applications such as production planning, portfolio selection and subset selection in regression. We propose a…

The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…

In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…