fa Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <span style="font-size:11pt"><span style="line-height:normal"><span style="text-autospace:none"><span style="font-family:&quot;Times New Roman&quot;,serif"><i><span style="font-size:10.0pt"><span style="color:black"><span style="letter-spacing:-.25pt">Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities in a way such that some criteria such as transportation costs, customer traveling distance, total service time, and cost of servicing are optimized. In this paper, we investigate the goal Weber location problem in which the location of a number of demand points on a plane is given, and the ideal is locating the facility in the distance </span></span></span></i><m:omath><m:ssub><m:ssubpr><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><span style="font-style:italic"><m:ctrlpr></m:ctrlpr></span></span></span></span></span></m:ssubpr><m:e><i><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><m:r>R</m:r></span></span></span></span></i></m:e><m:sub><i><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><m:r>i</m:r></span></span></span></span></i></m:sub></m:ssub></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span style="font-family:&quot;Times New Roman&quot;,serif"><span style="position:relative"><span style="top:4.0pt"> </span></span></span></span></span><i><span style="font-size:10.0pt"><span style="color:black"><span style="letter-spacing:-.25pt">, from the i-th demand point. However, in most instances, the solution of this problem does not exist. Therefore, the minimizing sum of errors is considered. The goal Weber location problem with the </span></span></span></i><m:omath><m:ssub><m:ssubpr><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><span style="font-style:italic"><m:ctrlpr></m:ctrlpr></span></span></span></span></span></m:ssubpr><m:e><i><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="i"></m:sty></m:scr></m:rpr>l</m:r></span></span></span></span></i></m:e><m:sub><i><span style="font-size:10.0pt"><span style="font-family:&quot;Cambria Math&quot;,serif"><span style="color:black"><span style="letter-spacing:-.25pt"><m:r>p</m:r></span></span></span></span></i></m:sub></m:ssub></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span style="font-family:&quot;Times New Roman&quot;,serif"><span style="position:relative"><span style="top:5.5pt"> </span></span></span></span></span><i><span style="font-size:10.0pt"><span style="color:black"><span style="letter-spacing:-.25pt">&nbsp;norm is solved using the stochastic version of the LBFGS method, which is a second-order limited memory method for minimizing large-scale problems. According to the obtained numerical results, this algorithm achieves a lower optimal value in less time with comparing to other common and popular stochastic optimization algorithms. Note that although the investigated problem is not strongly convex, the numerical results show that the SLBFGS algorithm performs very well even for this type of problem.</span></span></span></i></span></span></span></span><br> &nbsp; Goal Weber location problem, Quasi Newton algorithms, LBFGS methods, Stochastic optimization methods 1 19 http://iors.ir/journal/browse.php?a_code=A-10-1422-28&slc_lang=fa&sid=1 Aria Soleimani Kourandeh Aria Soleimani Kourandeh aria.soleimani@gmail.com 1111111111 1111111111 No Shahrood University of Technology, Shahrood, Iran Shahrood University of Technology, Shahrood, Iran Jafar Fathali Jafar Fathali fathali@shahroodut.ac.ir 1111111111 1111111111 Yes Shahrood University of Technology, Shahrood, Iran Shahrood University of Technology, Shahrood, Iran Sara Taherifard Sara Taherifard sara_taherifard@alum.sharif.edu 1111111111 1111111111 No Sharif University of Technology, Tehran, Iran Sharif University of Technology, Tehran, Iran