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Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
This article considers the challenge of accommodating outlier measurements in state estimation. The Risk-Averse Performance-Specified (RAPS) state estimation approach addresses outliers as a measurement selection Bayesian risk minimization…
In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
We study the restricted inverse optimal value problem on linear programming under weighted $l_1$ norm (RIOVLP $_1$). Given a linear programming problem $LP_c: \min \{cx|Ax=b,x\geq 0\}$ with a feasible solution $x^0$ and a value $K$, we aim…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
A popular approach to sentence compression is to formulate the task as a constrained optimization problem and solve it with integer linear programming (ILP) tools. Unfortunately, dependence on ILP may make the compressor prohibitively slow,…
This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in…
For the constrained LiGME model, a nonconvexly regularized least squares estimation model, we present an iterative algorithm of guaranteed convergence to its globally optimal solution. The proposed algorithm can deal with two different…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved inexact ALM (iALM) and conduct a unified analysis for…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…