Related papers: Implementing a smooth exact penalty function for g…
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 consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of…
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…
In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…
We propose a novel penalty method framework for the non-self-adjoint topology optimization problems, taking compliant mechanism problems as an example, by incorporating a convex nonlocal perimeter approximation scheme. We rigorously analyze…
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…