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We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
A novel matching based heuristic algorithm designed to detect specially formulated infeasible zero-one IPs is presented. The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive…
The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…
We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…
We present quasi-optimal a priori error estimates for general mixed finite element methods to approximate solutions of the Stokes problem subject to inhomogeneous Dirichlet boundary conditions. For the Scott-Vogelius element this yields…
In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods and artificial compression methods. Its form makes it an interesting option to replace the pressure update in the Uzawa iteration. The result, for the Stokes…
The paper is devoted to the penalty cell-centered finite element scheme (pFECC)on general meshes for the stationary Stokes problems with an incompressible variable viscosity and Dirichlet boundary conditions. In the objectives of this work,…
In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are…
In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate…