Many of the oldest and more prominent examples of NPTIME-complete decision problems arose from the study of combinatorial optimization problems, the NPTIME-completeness reflecting the apparent intractability of the optimization problem. More precisely, the NPTIME-completeness of the decision problem ruled...
Two Types of Methods to Resolve N-Dimensional Optimization ProblemsGiven a nonlinear, continuous and smooth function f : ; R n → R and the optimization problem f ( x ∗ ) = min x ∈ S f ( x ) , there are two types of methods which we'll cover in this class:...
Optimization problems with discrete variables are known as combinatorial optimization problems. If the variables in the problem are continuous, we can use calculus to solve the problem. A continuous optimization problem can be defined using the following standard form as an objective function (the ...
This chapter discusses the various approaches of optimization. Only basic calculus is needed to solve the formulated problems in all the examples furnished in this chapter. The focus is on illustrating the formulation of the problem at hand. The chapter looks at the formulation and optimization in...
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples Roshchina. The directed and Rubinov sub- differentials of quasidifferentiable functions. Part II: Calculus. Nonlinear Anal., 75(3):1058-1073, 2012. ... R Baier,E Farkhi,V Roshchina - ...
Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs ...
Peskir, G., Shiryaev, A.: Optimal Stopping and Free-Boundary Problems. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel (2006) MATH Google Scholar Rogers, L., Williams, D.: Diffusions, Markov processes, and Martingales Vol 2: Itô Calculus. Cambridge Mathematical Library. Camb...
We may use this property to convert maximization problems to minimization problems by multiplying f(x) by −1, as explained earlier in Section 2.11. The effect of scaling and adding a constant to a function is shown in Example 4.19. In Examples 4.20 and 4.23, the local minima for a ...
calculus, as it will be clear in the next section. As it will become clear in the subsequent sections, some Lipschitz-type properties will also play a central role in the main results. Hence, we introduce some useful concepts. A set-valued mapping\(\varPsi : \mathbb {R}^{n}\right...
Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition We introduce the notion of strong local minimizer for the problems of the calculus of variations on time scales. Simple examples show that on a time scale ... AB Malinowska,DFM Torres - 《Proceedings ...