**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Optimisation Problem: Solving by FM

Description

This lecture covers the modelling and optimization of energy systems, focusing on solving optimization problems with constraints and variables. Topics include linear and integer programming, convex and concave functions, Lagrange formulation, and indirect search methods.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (54)

In course

Instructor

Convex function

In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain.

Linear programming

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

Quasiconvex function

In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the of any set of the form is a convex set. For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints. The negative of a quasiconvex function is said to be quasiconcave. All convex functions are also quasiconvex, but not all quasiconvex functions are convex, so quasiconvexity is a generalization of convexity.

Integer programming

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.

Concave function

In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex. A real-valued function on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any and in the interval and for any , A function is called strictly concave if for any and . For a function , this second definition merely states that for every strictly between and , the point on the graph of is above the straight line joining the points and .

ME-454: Modelling and optimization of energy systems

The goal of the lecture is to present and apply techniques for the modelling and the thermo-economic optimisation of industrial process and energy systems. The lecture covers the problem statement, th

Related lectures (79)

Optimization Problems: Path Finding and Portfolio AllocationMGT-483: Optimal decision making

Covers optimization problems in path finding and portfolio allocation.

Optimization Programs: Piecewise Linear Cost FunctionsMGT-483: Optimal decision making

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Optimization Methods: Theory DiscussionME-454: Modelling and optimization of energy systems

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Optimisation in Energy SystemsME-454: Modelling and optimization of energy systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Thermodynamic Properties: Equations and ModelsME-454: Modelling and optimization of energy systems

Explains thermodynamic properties, equations of state, and mixture rules for energy systems modeling.