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 jointly sparse solution. Actually, computational studies have showed that the solution of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$l_p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mi>p</mi> </msub> </math> </EquationSource> </InlineEquation>-minimization (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$0>p>1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>0</mn> <mo>></mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>) is sparser than that of <InlineEquation ID="IEq9"> <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>-minimization. The generalized <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$$l_{2,p}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>-minimization (<InlineEquation ID="IEq11"> <EquationSource Format="TEX">$$p\in (0,1]$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math> </EquationSource> </InlineEquation>) is naturally expected to have better sparsity than <InlineEquation ID="IEq12"> <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>-minimization. This paper presents a type of models based on <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$$l_{2,p}\ (p\in (0, 1])$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mspace width="4pt"/> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>∈</mo> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> matrix norm which is non-convex and non-Lipschitz continuous optimization problem when <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation> is fractional (<InlineEquation ID="IEq15"> <EquationSource Format="TEX">$$0>p>1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>0</mn> <mo>></mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>). For all <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation> in <InlineEquation ID="IEq17"> <EquationSource Format="TEX">$$(0, 1]$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math> </EquationSource> </InlineEquation>, a unified algorithm is proposed to solve the <InlineEquation ID="IEq18"> <EquationSource Format="TEX">$$l_{2,p}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>-minimization and the convergence is also uniformly demonstrated. In the practical implementation of algorithm, a gradient projection technique is utilized to reduce the computational cost. Typically different <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$$l_{2,p}\ (p\in (0,1])$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>l</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mspace width="4pt"/> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>∈</mo> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> are applied to select features in computational biology. Copyright Springer Science+Business Media New York 2014