In this paper we consider nonlinear integer optimization problems. Nonlinear integer programming has mainly been studied for special classes, such as convex and concave objective functions and polyhedral constraints. In this paper we follow an other approach which is not based on convexity or concavity...
If we observe the function we will see its a parabola, i.e, the function is convex in nature. This convex function is the principle used in Gradient Descent to obtain the value of the model parameters The image shows the loss function. To get the correct estimate of the model parameters...
If we observe the function we will see its a parabola, i.e, the function is convex in nature. This convex function is the principle used in Gradient Descent to obtain the value of the model parameters The image shows the loss function. To get the correct estimate of the model parameters...
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that...
Mathematical programming includes linear programming (LP), nonlinear programming (NLP), and mixed integer programming (MIP). The following solving capabilities are supported: LP, convex quadratic programming (QP), semidefinite programming (SDP), and mixed-integer linear programming (MILP). More ...
If you are not an expert in convex optimization and linear programming, why not give it a try. Genetic algorithm is always a good solution to optimization problem. import geatpy as ea import numpy as np n = 10 np.random.seed(3) a = np.random.randint(1, 10, size=n) b = np....
Since the function − log(·) is convex, it follows from Jensen's inequality that D(p1 p2) = − p1(y) log y p2(y) p1(y) ≥ − log y p1(y) × p2(y) p1(y) = 0. This argument shows that the KL divergence is always nonnegative and that it is zero if and only if ...
Karush–Kuhn–Tucker (KKT) approach (for NLP) Useful (and necessary) for checking the optimality of a solution Not sufficient if the objective function is non-convex Most of these methods, such as the branch-and-bound algorithm, are exact. Exact optimization techniques are guaranteed to find ...
The polynomiality of nonlinear separable convex (concave) optimization problems, on linear constraints with a matrix with "small" subdeterminants, and the polynomiality of such integer problems, provided the inteter linear version of such problems ins polynomial, is proven. This paper presents a gen...
Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors represented by a NDD is proved to be an effectively computable con...