What is bilinear optimization?

The bilinear optimization (or bilinear programming) problem is a specially structured quadratic programming problem, where two sets of variables have bilinear relationships. Then, detection of unboundedness of bilinear programming problems is discussed when feasible region(s) are unbounded.

What is a bilinear term?

: linear with respect to each of two mathematical variables specifically : of or relating to an algebraic form each term of which involves one variable to the first degree from each of two sets of variables.

What is bilinear matrix inequality?

A linear matrix inequality (LMI) is a convex con- straint. Most control problems of inter- est that cannot be written in terms of an LMI can be written in terms of a more general form known as a bilinear matrix inequality (BMI).

What is constraint method?

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables.

What is a bilinear function?

From Wikipedia, the free encyclopedia. In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.

Is bilinear convex?

In [6], the convex hull of the bilinear function over D-polytopes is derived in the space of original variables.

What is a bilinear relationship?

In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v)

What is bilinear upsampling?

Bilinear Interpolation : is a resampling method that uses the distanceweighted average of the four nearest pixel values to estimate a new pixel value. The four cell centers from the input raster are closest to the cell center for the output processing cell will be weighted and based on distance and then averaged.

What is a chance constraint?

It is a formulation of an optimization problem that ensures that the probability of meeting a certain constraint is above a certain level. In other words, it restricts the feasible region so that the confidence level of the solution is high.

What is a hard constraint?

Hard constraints override logical relationships and thereby prevent activities from being scheduled according to the logic. Hard constraints should only be used when they reflect real dates. Examples of hard constraints are Mandatory Start and Mandatory Finish.

What is bilinear material?

Bilinear means there are two straight lines, one is the elastic line, which is defined by Isotropic Elasticity, the other is the plastic line. You are correct that entering 0 for the Tangent modulus creates an Elastic-Perfectly Plastic material.

What is bilinear problem?

In mathematics, a bilinear program is a nonlinear optimization problem whose objective or constraint functions are bilinear. An example is the pooling problem.

Can a bilinear form be extended to include modules?

The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms. When K is the field of complex numbers C, one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.

When is a bilinear form said to be non-degenerate?

For a finite-dimensional vector space V, if either of B1 or B2 is an isomorphism, then both are, and the bilinear form B is said to be nondegenerate. More concretely, for a finite-dimensional vector space, non-degenerate means that every non-zero element pairs non-trivially with some other element:

When is a function called a bilinear function?

A functionf(x;y) is called bilinear if it reduces to a linear one by flxing the vectorxory to a particular value. In general, a bilinear function can be represented as follows: f(x;y) =aTx+xTQy+bTy; wherea;x 2Rn,b;y 2Rm, andQis a matrix of dimensionn £ m. It is easy to see that bilinear functions compose a subclass of quadratic functions.

Can a bilinear form be a skew-symmetric part?

A bilinear form is symmetric if and only if the maps B1, B2: V → V∗ are equal, and skew-symmetric if and only if they are negatives of one another. If char(K) ≠ 2 then one can decompose a bilinear form into a symmetric and a skew-symmetric part as follows. where tB is the transpose of B (defined above).