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Questions tagged [optimization]

general questions about selecting a best element from some set of available alternatives.

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Non-convex optimization with correlated minima

I am thinking of non-convex optimization problems where the minima are somehow correlated. Maybe there are symmetry relationships among minima or maybe there is regularity in spacing among minima in ...
Omar Shehab's user avatar
0 votes
0 answers
69 views

What work on min max connectivity problems has there been?

For instance has min max spanning/steiner/prize-collecting tree been studied. i.e. each edge $e$ has costs $c_{v,e}$ of each resource $i$. And we wish to find a spanning tree minimizing the maximum ...
Hao S's user avatar
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64 views

Has multiobjective prize collecting steiner tree or TSP been studied?

Suppose we have a graph $G$ a root $r$ and each node $v$ has some amount of $c_{v,i}$ of each resource $i$. I connect a set of nodes to the root that maximizes the minimum amount of any resource using ...
Hao S's user avatar
  • 228
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cutting plane method for convex optimization

The cutting plane approach in convex optimization is a general recipe for minimizing a convex function. The argument relies on the fact that using the gradient vector, we can cut the feasible set into ...
MMH's user avatar
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-1 votes
1 answer
52 views

Computability/Complexity of optimization problems in general

Dear StackExchange community, I have a question, or better phrased I am confused and would like to be enlightened by you! So assume we have a (optimization) problem like that: Instance: Let $f:\...
Thinklex's user avatar
1 vote
0 answers
39 views

Convergence rates for the iterates of SGD on Lipschitz convex functions

Let $f:X \rightarrow \mathbb{R}$ be a convex and $L$-Lipschitz continuous function. Suppose $f^* = \min_{x \in X} f(x) \in \mathbb{R}$ and let $X^* = \{x \in X : f(x) = f^*\}$. For a non-negative ...
Andrea's user avatar
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1 vote
0 answers
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Placing a circle in a point cloud

I need to place a circle with fixed radius in a cloud of points. The circle also must lay in a polygon (the points are also in that polygon) This circle has to contain as many points as possible. Are ...
fanda's user avatar
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3 votes
0 answers
71 views

Hardness of Approximation for Three Matroid Intersection

I am searching for the best known hardness of approximation bound for three matroid intersection. The input is three matroids on the same ground set which are accessible using three different ...
MatroMan's user avatar
4 votes
1 answer
213 views

Is Optimal Swap Sorting NP-Hard?

Given an array of integers with duplicates, find the minimum number of swaps to sort the array. According to this question, the problem is NP-Complete but the reference given proves NP-Completeness ...
Daniel García's user avatar
3 votes
2 answers
166 views

Given a weighted graph with $pk$ nodes find a min weight forest with $p$ components each containing exactly $k$ nodes

Given a weighted graph with $pk$ nodes find a min weight forest with $p$ components each containing exactly $k$ nodes. Does this have a constant approximation? ($p,k$ and the graph are all part of the ...
Hao S's user avatar
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2 votes
1 answer
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Maximum cardinality disjoint cycle cover in undirected graphs

I call a maximum cardinality disjoint cycle cover of a graph a vertex-disjoint cycle cover containing the maximum possible number of cycles in the graph. What is known about the complexity of this ...
delete000's user avatar
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Is there an algorithm that finds a minimum vertex cover with an approximation factor of 3/2 for a planar graph?

Is there an algorithm that finds a minimum vertex cover with an approximation factor of 3/2 for a planar graph?
John Stuart's user avatar
2 votes
1 answer
117 views

Is beta normalization used for program optimization?

Beta normalization reduces a lambda term to its beta normal form, if it exists. The beta normal form is a computationally equivalent term with no "redundant" computation, in a sense; for ...
Hirrolot's user avatar
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0 answers
32 views

Nonlinear GAP similar to Min-GAP but with minimum quantities and without capacity

I have $m$ items and $n$ bins where each item $i$ and bin $j$ has a value $v_{i,j}$. Each bin $j$ has a value $V_j$. I want to pack the items into the bins such that (1) I minimize the ratio of the ...
Jika's user avatar
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2 votes
2 answers
133 views

Linear Programming Sensitivity to Matrix

Consider a linear program in the following standard form: \begin{align*} &\max c^T x &\\ &\mbox{subject to:}\\ &A x \preceq b\\ &x \succeq 0 \end{align*} Its dual is \begin{align*}...
sd234's user avatar
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4 votes
0 answers
134 views

Which variant of the ellipsoid method was used for the Santa Claus problem?

As one of the steps in the article The Santa Claus problem (Bansal and Sviridenko, 2006) the following linear problem was considered (at the end of the second page, as the dual): \begin{align*} &\...
eden hartman's user avatar
2 votes
1 answer
101 views

Approximating the utilitarian welfare minus a constant

Assume we have $n$ agents and $m$ indivisible goods that need to be allocated among the agents such that their sum of utilities is maximized. Denote the set of allocations by $\mathcal{A}$ and the ...
eden hartman's user avatar
2 votes
0 answers
43 views

Submodulare welfare maximization: is an additive approximation algorithm known?

Sudmodular welfare maximization is the problem of allocating items among agents with different valuations, represented by submodular set functions, such that the sum of agents' values is as large as ...
Erel Segal-Halevi's user avatar
-1 votes
1 answer
74 views

Find Combinations of fibonacci values to approximate a target value given $F(A,B,C,D) = (A + B + C) / D$

I am able to solve this using brute force but curious if there is a better approach. Given the function $F(A,B,C,D) = (A + B + C) / D$ where each variable is in the first 7 distinct values of the ...
john doe's user avatar
1 vote
0 answers
25 views

Optimization: Turning a sparse graph of probabilities into the maximum likelihood DAG

I have a sparse matrix of probabilities that I want to turn into a DAG. If x[m,n] = pr it means that m is a descendent (direct or transitively) of n with probability pr. I want to construct a DAG over ...
Joseph Turian's user avatar
1 vote
0 answers
32 views

Justification of smoothness of component functions

In stochastic optimization, the common objective is to minimize $f(x) = \frac 1N \sum_{i=1}^N f_i(x)$ (there is a different formulation, but it doesn't matter for this question). For nonconvex ...
Dmitry's user avatar
  • 201
-2 votes
1 answer
256 views

What is the reason to believe that quantum heuristic algorithms can solve NP-Complete problems?

There is an ever going trend to believe that a large number of NP-Complete or NP-Hard problems can be solved using quantum heuristics. I have observed, a common trend, to take any sort of ...
Marion's user avatar
  • 183
3 votes
1 answer
229 views

Complexity class of optimization problems whose fractional relaxation is polynomial-time solvable

It is known that the problem of integer linear programming is NP-hard, but its fractional relaxation can be solved in polynomial time. The concept of fractional relaxation can be applied to any ...
Erel Segal-Halevi's user avatar
1 vote
1 answer
112 views

How to calculate processor throughput boundary in CSAPP?

In Chapter 5.7 of CSAPP, author list out the throughput boundary of Intel Core i7 Haswell while executing the operation Integer addition and multiplication, floating points addition and multiplication....
陳柔妍's user avatar
0 votes
1 answer
185 views

Solving Grouped Weighted Job Scheduling with Release Times and Deadlines on a Single Machine with Multiple Availability Intervals

I'm working on a scheduling problem where I need to schedule a set of n weighted jobs that are partitioned into m groups, where ...
beardeadclown's user avatar
0 votes
1 answer
76 views

An inequality about median of points in higher dimensions

Let $S$ be a set of points in $\mathbf{R^d}$ and let $m$ be the median of this set of points, i.e. $\sum_{x \in S} || x - y||$ is minimized when we have $y=m$. Now let $z$ be an arbitrary point in $\...
David's user avatar
  • 1
3 votes
1 answer
224 views

Can the ellipsoid method be used with a randomized separation oracle?

Suppose we are trying to solve the following optimization problem: $$ \text{maximize } ~~ c\cdot y \\ \text{subject to } ~~ y\in S $$ where the region $S$ is described by an exponential number of ...
eden hartman's user avatar
4 votes
0 answers
80 views

Submodular welfare maximization: what is the best known approximation ratio of a deterministic algorithm?

In the submodular welfare maximization problem, there is a set $M$ of items that should be partitioned among $n$ agents. Each agent $i$ has a value function $v_i: 2^M\to \mathbb{R}_+$. All value ...
Erel Segal-Halevi's user avatar
0 votes
0 answers
95 views

How to prove that a given class of convex programs cannot be solved by linear programming?

Given the following program, where $f, g$ are convex functions: $$ \text{minimize}~~ f(x) \\ \text{subject to}~~ g(x)\leq 0 $$ the problem can be solved by convex programming algorithms, but it would ...
Erel Segal-Halevi's user avatar
0 votes
0 answers
40 views

Computational complexity of CVaR calculation

I am currently looking for literature discussing the computational complexity of CVaR calculation. At this point the only work I have found is the following. Mavronicolas, Marios, and Burkhard Monien. ...
Omar Shehab's user avatar
3 votes
1 answer
195 views

Solving linear programs with special structure

We have an application and at some point we need to solve a linear programming problem that looks like this: $$ \min\ w_{1,2} + w_{3,4} + w_{5,6}\\ x_i - x_j \leq c_{ij},\ \forall\ (i,j) \in C\\ x_1 - ...
Maltus's user avatar
  • 73
3 votes
2 answers
223 views

What is this graph problem, and how hard is it?

My problem is quite simple to state, so it surely must have a name: Given a graph $G=(V,E)$ with edge weights $w(e) \in \mathbb{Z}$, find a $V' \subseteq V$ that maximizes $\sum_{e \in E' } w(e)$, ...
tobwin's user avatar
  • 31
1 vote
1 answer
82 views

A bound that follows from submodularity

I am studying Lemma 1 of this paper: The Adaptive Complexity of Maximizing a Submodular Function. The proof appears on page 11. I got stuck on this inequality: where $f$ is a monotone submodular set ...
Null_Space's user avatar
1 vote
0 answers
93 views

How to solve the following continuous optimization problem?

Consider a function $f: X\times Y\times N$, where $X, Y \subseteq \mathbb{R}^m$ are convex sets, and $N = \{1,2,\dots,n\}$. We additionally know that $f(\cdot,y,S)$ is convex for fixed $y,S$ $f(x,\...
ashtavakra's user avatar
1 vote
0 answers
66 views

Unbounded Knapsack Instance with a Single Optimum that takes each Item Once?

Consider the Unbounded Knapsack Problem (UKP): We are given a set of $n$ items $I = \{1,\ldots,n\}$ of integral weights $w_1, \ldots, w_n \in \mathbb{N}$, integral profits $p_1, \ldots, p_n \in \...
John's user avatar
  • 412
0 votes
0 answers
59 views

Uniformly redistributing items across bins. What problem is this?

I'm trying to find reading material on a particular problem I'm interested in, but I don't know the terms to search. Problem assumptions/definitions: We have finite number of items I with weights [0, ...
Lycus's user avatar
  • 101
1 vote
0 answers
46 views

Will the maximum entropy joint distribution given a known set of marginal distributions have the maximum plausible support?

Define $[n] = \{1, 2, ..., n\}$. Given a distribution $P : \{0, 1\}^{[n]} \rightarrow [0, 1]$ and a subset $S \subseteq [n]$, we can define the $S$-marginal of $P$, $P_S : \{0, 1\}^S \rightarrow [0, 1]...
Samuel Schlesinger's user avatar
1 vote
0 answers
83 views

Packing k vertex trees

Consider a graph $G=(V,E)$ with $n$ vertices. What do we know about packing of $k$ vertex trees, Both integral and fractional packing are interesting. $k=2$, it is just the number of edges, hence ...
Chao Xu's user avatar
  • 4,479
0 votes
0 answers
26 views

Quantifying the cost of procedures

Is there any research on quantifying the cost of a procedure, with regard to compiler optimization? I.e. assigning some kind of cost in terms of CPU time or memory to a procedure, either so the ...
Ari Fordsham's user avatar
3 votes
0 answers
78 views

Solving MDPs with polytope action spaces

A (finite) Markov Decision Process (MDP) consists of a finite set of states $S$, a finite set of actions $A_s$ which we will allow to depend on the state $s\in S$, an initial state $s_0\in S$ (the ...
Vanessa's user avatar
  • 2,151
1 vote
0 answers
55 views

Find the minimum cost spider joining a root to some leaves

A spider is a tree with at most one vertex of degree greater than 2. This vertex is called the head of the spider. I am interested in the following problem: We are given an undirected graph $G = (V,E)$...
Karagounis Z's user avatar
1 vote
0 answers
61 views

The tree augmentation problem, but with hyperlinks

In the (Weighted) Tree Augmentation Problem, we are given a tree $T = (V,E)$ and a set of additional edges $L$ called links with non-negative costs. Each link $\ell = (u,v)$ covers the tree edges ...
Karagounis Z's user avatar
4 votes
1 answer
208 views

Tensor network contraction "bubbling": why are some approaches more computationally efficient than others (question from a beginner)

I am learning the very basics of tensor network theory and I am trying to understand why some ways to contract tensors are better than others in terms of computational complexity. Knowing in which ...
Marco Fellous-Asiani's user avatar
1 vote
2 answers
106 views

Growth rate of Knapsack Solutions

Let's say I have a Knapsack with capacity $\tau$, and I have an infinite sequence of items with weights $(a_n)_{n=1}^{\infty}$. A feasible Knapsack solution is a subset $S \subset \mathbb{N}$ such ...
Asterix's user avatar
  • 617
2 votes
1 answer
211 views

Maximize a special monotone submodular function - is it easier?

I am looking for a way to optimize the function $f$, defined below. First, fix some positive integer $k$ and let $c_1$ and $c_2$ be non-negative vectors in $\mathbb{R}^n$. Let $g$ be an increasing ...
Karagounis Z's user avatar
0 votes
0 answers
82 views

Parameterized Complexity of Vertex Multicut

Let $G$ be an undirected graph, $\{(s_1,t_1),\dots,(s_k,t_k)\}$ a collection of pairs of vertices, and $p$ an integer. The Vertex Multicut problem asks if there is a set $S$ of at most $p$ vertices ...
BBK's user avatar
  • 103
2 votes
1 answer
135 views

Optimization problems where the solver can choose which variables are continuous

A typical optimization problem looks like the following, where $f$ represents the objective and $g$ the constraints: $$ \text{maximize}~~~f(x1,\ldots,x_n)~~~\text{subject to}: \\ g(x_1,\ldots,x_n)=0, \...
Erel Segal-Halevi's user avatar
3 votes
1 answer
161 views

Is there an approximate version of the strong duality theorem for linear programming?

Consider the following dual linear programs: $$ \min \mathbf{c^T x} ~~ \text{s.t.} ~~ A \mathbf{x} \geq \mathbf{b}, \mathbf{x}\geq 0; \\ \max \mathbf{b^T y} ~~ \text{s.t.} ~~ A^T \mathbf{y} \leq \...
Erel Segal-Halevi's user avatar
2 votes
0 answers
130 views

Does the standard 4/3 integrality gap for TSP example work for Euclidean TSP?

Given a graph $G=(V,E)$, costs $c \in \mathbb{R}^E$ the TSP problem is to compute a min cost tour of the graph. The LP is min $ c^tx $ $x(\delta(S)) \geq 2 \ \ \ \ \forall S \subset V $ $x(\delta(v)...
Hao S's user avatar
  • 228
2 votes
0 answers
116 views

Can this relaxed subset-sum problem be solved with a smaller dynamic program? [closed]

Cross-post from CS.SE In the subset sum problem, the input is a list of positive integers $x_1,\ldots,x_n$ and an integer $T$, and the goal is to decide whether there is a subset of sum exactly $T$. ...
Erel Segal-Halevi's user avatar

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