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TY  - JOUR
AU  - Kishore, Rajeev
PY  - 2010/09/23
Y2  - 2025/09/23
TI  - Mathematical Science Reformulate Convex Relaxation in Logic Based Optimization
JF  - Journal of Experimental Sciences
JA  - JES
VL  - 1
IS  - 5
SE  - Formal Sciences
DO  - 
UR  - https://www.updatepublishing.com/journal/index.php/jes/article/view/1729
SP  - 
AB  - &lt;div style=&quot;border-right: medium none; padding-right: 0in; border-top: medium none; padding-left: 0in; padding-bottom: 1pt; border-left: medium none; padding-top: 0in; border-bottom: windowtext 1pt solid; mso-element: para-border-div; mso-border-bottom-alt: solid windowtext .5pt;&quot;&gt;&lt;span style=&quot;font-size: 6pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 6pt 0in 0pt; text-align: justify; mso-layout-grid-align: none;&quot;&gt;&lt;strong&gt;&lt;span style=&quot;font-size: 10pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Abstract &lt;/span&gt;&lt;/strong&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 6pt 0in 0pt; text-align: justify; mso-layout-grid-align: none;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;We present a convex conic Relaxation for a problem of maximizing an indefinite quadratic form over a set of, convex constraints on the squared variables, convex envelopes of non convex functions are widely used to calculate lower bounds of solutions of non linear programming problem (NLP). This paper proposes a non linear continuous convex envelope for (Linear, bilinear, trilinear fractional) monomial terms of odd degree and the range of variables (x, y, z) includes zero. &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt; text-align: justify; mso-layout-grid-align: none;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;We also drive a linear relaxation from the proposed envelope and computer both the Linear and non linear formulations with relaxations obtained using other approaches.&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt; text-indent: 31.5pt; text-align: justify; mso-layout-grid-align: none;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Â &lt;/span&gt;&lt;/p&gt;&lt;div style=&quot;border-right: medium none; padding-right: 0in; border-top: medium none; padding-left: 0in; padding-bottom: 1pt; border-left: medium none; padding-top: 0in; border-bottom: windowtext 1pt solid; mso-element: para-border-div; mso-border-bottom-alt: solid windowtext .5pt;&quot;&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt; text-align: justify; mso-layout-grid-align: none; mso-padding-alt: 0in 0in 1.0pt 0in; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in;&quot;&gt;&lt;strong&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Keywords&lt;/span&gt;&lt;/strong&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;: Odd degree, Monomial, Convex relaxation, Global optimization &lt;/span&gt;&lt;/p&gt;&lt;/div&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt; text-align: justify; mso-layout-grid-align: none; mso-padding-alt: 0in 0in 1.0pt 0in; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in;&quot;&gt;Department of Mathematic, Jamuna Prasad Memorial Degree College, Bareilly&lt;/p&gt;&lt;/span&gt;&lt;/div&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt 0.25in; text-indent: -0.25in; text-align: justify;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Please Cite This Article As:&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt 0.25in; text-indent: -0.25in; text-align: justify;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Rajeev Kishore. 2010. Mathematical Science Reformulate Convex Relaxation in Logic Based Optimization. J. Exp. Sci. 1(5):25-27.&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt 0.25in; text-indent: -0.25in; text-align: justify;&quot;&gt;&lt;span style=&quot;font-size: 8pt; font-family: &quot;;Tahoma&quot;;,&quot;;sans-serif&quot;;;&quot;&gt;Â &lt;/span&gt;&lt;/p&gt;
ER  -