Matlab Linear programming; how to minmize maximum of decision variable?

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I am trying to minimize and objective function. It is a multiobjective function using weighted sum option. One of the objectives is to minimize the maximum of the decision variable. However, the maximum of decision variable is not know prior and i cannot use the 'max(decisionvariable)' command in optimization tool box. I am using Problem-Based Optimization tool box, so is there a way to replace the xommand to find maximum of decision variable? Problem Description: I have energy consumption data for 24 hours. I want to reduce the peak of the load after shifting the load to different times. Its also known as peak to average ration minimization. I need to minimize the peak of load after shifting bu i cannot include 'max' or 'mean' in the objective function. My variables are load values 'L' 1*48 matrix (half hourly energy records), Price 'P' again 48 values. I want to minimize the cost of energy consumed during 24 hours which is cost=L*P and i want to achieve this with minimum peak value of the L.
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zafar khan
zafar khan on 11 Sep 2018
My variables are load values 'L' 1*48 matrix (half hourly energy records), Price 'P' again 48 values. I want to minimize the cost of energy consumed during 24 hours which is cost=L*P and i want to achieve this with minimum peak value of the L.

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Answers (2)

Steven Lord
Steven Lord on 11 Sep 2018
Consider the fminimax function in Optimization Toolbox.
  2 Comments
Matt J
Matt J on 11 Sep 2018
Edited: Matt J on 12 Sep 2018
Problem-based optimization is not appropriate for your situation. It is for single-objective linear programming only. You appear to have two objectives ( namely you are minimizing both P*L and max(L) ), one of which is non-linear.

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Matt J
Matt J on 11 Sep 2018

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