Recently, matrix norm <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$l_{2,1}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </math> </EquationSource> </InlineEquation> has been widely applied to feature selection in many areas such as computer vision, pattern recognition, biological study and etc. As an extension of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$l_1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation> norm, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$l_{2,1}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </math> </EquationSource> </InlineEquation> matrix norm is often used to find...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper, we analyze the symmetric interior penalty Galerkin (SIPG) for distributed optimal control problems governed by unsteady convection diffusion equations with control constraint bounds. A priori error estimates are derived for the semi- and fully-discrete schemes by using piecewise...

We propose a new stochastic first-order algorithm for solving sparse regression problems. In each iteration, our algorithm utilizes a stochastic oracle of the subgradient of the objective function. Our algorithm is based on a stochastic version of the estimate sequence technique introduced by...

The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q <Subscript>0</Subscript>(x)→min, subject to an upper and lower bounded general quadratic constraint, ℓ≤q <Subscript>1</Subscript>(x)≤u. This means that there are no definiteness assumptions on either quadratic...</subscript></subscript>

The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to...

In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. Integrating...

In this paper, we propose a regularized Newton method without line search. The proposed method controls a regularization parameter instead of a step size in order to guarantee the global convergence. We show that the proposed algorithm has the following convergence properties. (a) The proposed...

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\ell _\tau $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mi mathvariant="italic">τ</mi> </msub> </math> </EquationSource> </InlineEquation> norms, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\tau \ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">τ</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, in the demand points. We analyze the difficulty of this family of problems and revisit...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\ell _1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation>-regularized least-squares approach that has...</equationsource></equationsource></inlineequation>