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Lecture

Certificates: Existence and Proving

In course

MATH-261: Discrete optimization

This course is an introduction to linear and discrete optimization. Warning: This is a mathematics course! While much of the course will be algorithmic in nature, you will still need to be able to prove theorems. ...

Description

This lecture covers the concept of certificates, focusing on proving the existence of a solution and the process of proving it. It delves into the constraints and linear programming, discussing the duality between minimization and maximization problems. The instructor explains the relationship between feasible solutions in different scenarios and the optimality of solutions in linear programs.

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Instructors (2)

Rom Pinchasi

Friedrich Eisenbrand

Friedrich Eisenbrand's main research interests lie in the field of discrete optimization, in particular in algorithms and complexity, integer programming, geometry of numbers, and applied optimization. He is best known for his work on efficient algorithms for integer programming in fixed dimension and the theory of cutting planes, which are an important tool to solve large scale industrial optimization problems in practice. Before joining EPFL in March 2008, Friedrich Eisenbrand was a full professor of mathematics at the University of Paderborn. Friedrich received the Heinz Maier-Leibnitz award of the German Research Foundation (DFG) in 2004 and the Otto Hahn medal of the Max Planck Society in 2001.

Official source

Ontological neighbourhood

Theoretical computer science

Algorithms and data structures: Combinatorial optimization

Related concepts (32)

Feasible region

In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.

Public key certificate

In cryptography, a public key certificate, also known as a digital certificate or identity certificate, is an electronic document used to prove the validity of a public key. The certificate includes information about the key, information about the identity of its owner (called the subject), and the digital signature of an entity that has verified the certificate's contents (called the issuer). If the signature is valid, and the software examining the certificate trusts the issuer, then it can use that key to communicate securely with the certificate's subject.

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.

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.

Extended Validation Certificate

An Extended Validation Certificate (EV) is a certificate conforming to X.509 that proves the legal entity of the owner and is signed by a certificate authority key that can issue EV certificates. EV certificates can be used in the same manner as any other X.509 certificates, including securing web communications with HTTPS and signing software and documents. Unlike domain-validated certificates and organization-validation certificates, EV certificates can be issued only by a subset of certificate authorities (CAs) and require verification of the requesting entity's legal identity before certificate issuance.

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